Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a...
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![Page 1: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/1.jpg)
![Page 2: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/2.jpg)
Let’s start by reviewing what you know …
![Page 3: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/3.jpg)
![Page 4: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/4.jpg)
Exponents … Powers• When you take a number
to a positive power, you multiply it by itself repeatedly.
![Page 5: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/5.jpg)
• 35 = 3•3•3•3•3 = 243
• 27 = 2•2•2•2•2•2•2 = 128
• (-4)3 = (-4)(-4)(-4) = -64
• (-3)2 = (-3)(-3) = 9
• 08 = 0•0•0•0•0•0•0•0 = 0
![Page 6: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/6.jpg)
Write 7•7•7•7•7 with exponents
![Page 7: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/7.jpg)
Write 7•7•7•7•7 with exponents
75
![Page 8: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/8.jpg)
The number that is taken to a power is called the base.
![Page 9: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/9.jpg)
Rules for working with exponents:
Product Rule• xn•xm = xn+m
• When you multiply things with exponents, add the exponents.
![Page 10: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/10.jpg)
• 32•34 = 36
• (59)(53) = 512
• n8•n8 = n16
![Page 11: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/11.jpg)
What is (w3x2y5z3)(x3yz6) ?
![Page 12: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/12.jpg)
What is (w3x2y5z3)(x3yz6) ?
w3x5y6z9
![Page 13: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/13.jpg)
What is (2x)(2y) ?
![Page 14: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/14.jpg)
What is (2x)(2y) ?
2x+y
![Page 15: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/15.jpg)
Quotient Rule
When you divide or make a fraction out of things with
exponents, subtract the exponents.
![Page 16: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/16.jpg)
• 59 53 = 56
• or just 7
![Page 17: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/17.jpg)
Power Rule• (xn)p = xnp
• When you raise a power to
a power, multiply the exponents.
![Page 18: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/18.jpg)
• (53)2 = 56
• (89)5 = 845
• (22)4 = 28
![Page 19: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/19.jpg)
What is (w2xy4z3)5 ?
![Page 20: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/20.jpg)
What is (w2xy4z3)5 ?
w10x5y20z15
![Page 21: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/21.jpg)
Zero Exponent Rule• x0 = 1• If you raise anything
(except 0) to the zero power, the answer is always 1.
• 30 = 1• 50 = 1• 100 = 1
![Page 22: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/22.jpg)
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You know that any fraction with the same numerator and denominator equals 1.
![Page 24: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/24.jpg)
But … when there are exponents in the fraction, you can subtract exponents.
If the numerator and denominator are the same, you get a zero exponent.
![Page 25: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/25.jpg)
Since these equal the same fractions, the zero exponents equal 1.
![Page 26: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/26.jpg)
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Negative Exponent Rule
•
• When you take something to a negative power, it makes a fraction (reciprocal).
![Page 28: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/28.jpg)
• 5-1 = 1/5
• 3-2 = 1/9
• 2-3 = 1/8
![Page 29: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/29.jpg)
Other Useful Rules …
(xy)p = xpyp
![Page 30: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/30.jpg)
For example …
503 = 53 x 103
= 125 x 1000= 125,000
![Page 31: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/31.jpg)
![Page 32: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/32.jpg)
Scientific Notation• a shorthand way to write
very large or very small numbers
• In scientific notation, numbers always have the form ____ X 10--.
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![Page 35: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/35.jpg)
![Page 36: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/36.jpg)
To change a number into scientific notation …
• Move the decimal so there
is just one place before it.
• Count the places after the decimal
![Page 37: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/37.jpg)
Example:
Change 53,700,000,000 to scientific notation
![Page 38: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/38.jpg)
Example:
Change 53,700,000,000 to scientific notation
5.37 x 1010
![Page 39: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/39.jpg)
Example:
Change 435,300,000 to scientific notation
![Page 40: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/40.jpg)
Example:
Change 435,300,000 to scientific notation
4.353 x 108
![Page 41: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/41.jpg)
• If the number is already a decimal, you still move the decimal so there is just one place before it.
• Count how many places you moved the decimal; the
exponent is negative that number. (This is always one more than the number of 0’s after the original decimal.)
![Page 42: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/42.jpg)
Example:
Change .000412 to scientific notation.
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Example:
Change .000412 to scientific notation.
4.12 x 10-4
![Page 44: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/44.jpg)
Example:Change .00000000000024 to scientific notation
![Page 45: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/45.jpg)
Example:Change .00000000000024 to scientific notation
2.4 x 10-13
![Page 46: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/46.jpg)
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To change back to decimal notation …• Copy the significant digits• If the exponent is positive, there
are that many places after the first digit; add zeros to make the number of places.
• If the exponent is negative, put in one fewer zeros than the exponent at the beginning.
![Page 48: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/48.jpg)
Example:Change 3.7 x 105 to decimal notation.
![Page 49: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/49.jpg)
Example:Change 3.7 x 105 to decimal notation.
370,000
![Page 50: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/50.jpg)
Example:Change 5.417 x 1012 to decimal notation.
![Page 51: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/51.jpg)
Example:Change 5.417 x 1012 to decimal notation.
5,417,000,000,000
![Page 52: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/52.jpg)
Example:Change 3.4 x 10-5 to decimal notation.
![Page 53: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/53.jpg)
Example:Change 3.4 x 10-5 to decimal notation.
.000034
![Page 54: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/54.jpg)
Example:Change 2.456 x 10-7 to decimal notation
![Page 55: Let’s start by reviewing what you know … Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.](https://reader035.fdocuments.in/reader035/viewer/2022062716/56649dd85503460f94acda42/html5/thumbnails/55.jpg)
Example:Change 2.456 x 10-7 to decimal notation
.0000002456