Multiplication Property of Exponents, Rational

Exponents and Scientific Notation

01-06-15

Multiplication Property of Exponents

(a3)(a4)

• This means

• Or a7

• A shortcut for this---• When you are multiplying and the

bases are the same ADD THE EXPONENTS

a a a a a a a

Examples

• (2.3 · )• Find the area of

the triangle:

• 1.15 · • 6

4x

3x

Try these…

• 6 · 3 · 2 • (9 · )(0.3 · )• (0.7 · )• · · 2q

• 36• 2.7 · • 2.1 · • 18

Rational Exponents

Rational Exponents

• Exponents expressed as fractions are called Rational Exponents.

• 32 means 3∙3, which equals 9. You can also represent this using a rational exponent: .

• In general, means that b multiplied as a factor n times equals a.

Examples

• find the number that when multiplied by itself four times gives you 81.

• 9∙9=81 and (3 ∙ 3)(3 ∙ 3)=81• So = 3

Try These:

2

5

3

2

Rational Exponents

• If the rational exponent has a numerator greater than one, that is the number of times you multiply each factor.

• == 2 ∙ 2 ∙ 2= 8

Scientific Notation

• A number is in scientific notation when• There is a number (I’ll call “n”) that is bigger

than or equal to one, but less than ten.• This number “n” is multiplied by a power of ten.• A power of ten is 10 to the something power.• So it will look something like this: (just

remember digit dot)• n• n. x 10 -3

Examples

Which are in scientific notation?3.5 x 103

62.6 x 10-2

0.86 x 108

3.82 x 100-6 4.6 x 100

Yes No No No Yes

Examples

Write in scientific notation

13,030,000 0.000 092 675 million 283 hundred

thousandths

1.303 x 107

9.2 x 10-5

6.75 x 108

2.83 x 10-3

Examples

Write in standard form (as a regular number):

6.2 x 10-5

1.2345 x 1010

7.91 x 100

5 x (7 x 106)

0.000 062 12,345,000,00

0 7.91 35,000,000

Multiplying Scientific Notation

• The Multiplication Property of Exponents can be used to multiple 2 numbers written in scientific notation because the base 10 is the same.