Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

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Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents

Transcript of Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Page 1: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Copyright (c) 2010 Pearson Education, Inc.

Laws of Exponents

Page 2: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 2

An exponent is a “shorthand” number that saves writing the multiplication of the same numbers.

433 3 3 3

exponent34

base

This is read “three to the fourth power.”

Exponents

Page 3: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 3

The Product Rule

Example) Multiply.

The Product RuleTo multiply two exponential expressions that have the same base, keep the base and add the exponents.

xa · xb = xa + b

The Product RuleTo multiply two exponential expressions that have the same base, keep the base and add the exponents.

xa · xb = xa + b

a.) c4 · c5 = c4 + 5 = c9

b.) 3a3 · a6 = 3a3 + 6 = 3a9 c.) 4w2 · 2w5 = (4)(2)w2 + 5 = 8w7

Page 4: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 4

The Quotient Rule

Example:Divide.

The Quotient Rule To divide two exponential expressions that have the same base, keep the base and subtract the exponents. .

The Quotient Rule To divide two exponential expressions that have the same base, keep the base and subtract the exponents. .

Remember that the base does not change.

aa b

bx xx

a.)6

233

6 2 43 3

Page 5: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 5

The Quotient Rule(by cancellation)

Example:Divide.

a.)2

633 4

3 3 13 3 3 3 3 3 3

b.)4

7z

z

31z z z z

z z z z z z z z

Quotient Rule

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Tobey & Slater, Beginning Algebra, 7e 6

Negative Exponents

Negative exponents determine POSITION of the expression.Negative exponents DO NOT change the sign of the expression.

Negative Exponent Properties:Negative Exponent Properties:

1nn

xx

1 nn

xx

nm

n m

yxy x

n nyx

y x

Page 7: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 7

Zero Power

The Zero Power Property:

, if x 0 (00 remains undefined).

The Zero Power Property:

, if x 0 (00 remains undefined).0 1x

Example Simplify:3 0

2a ba

1a a a aa a

Page 8: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 8

Raising a Power to a PowerTo raise a power to a power, keep the same base and multiply the exponents.

Raising a Power to a PowerTo raise a power to a power, keep the same base and multiply the exponents.

Raising Exponential Expressions to a Power

ba abx x

Example:Simplify. a.) (x5)3

b.) (y3)3

= x5·3 = x15

= y3·3 = y9

Page 9: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 9

Product Raised to a PowerProduct Raised to a Power

Product Raised to a Power

a a axy x y

c.) (4x3y2)3

Example:Simplify. a.) (2c)3

b.) (5xy)2

= 43x9y6 = 64x9y6

= (2)3c3 = 8c3

= (5)2(xy)2 = 25x2y2

Page 10: Copyright (c) 2010 Pearson Education, Inc. Laws of Exponents.

Tobey & Slater, Beginning Algebra, 7e 10

Quotient Raised to a PowerQuotient Raised to a Power

Quotient Raised to a Power

a a

ax xy y

if y 0.

Example:Simplify. a.)

4xy

4

4xy

b.)43

23ab

44 312

4 82

3 81a abb