Exponents

Review:

• Evaluate each expression:

1. 3³2.7¹3.-6²4.(⅜)³5.(-6)²6.3· 2³

• Answers

1. 272. 73. -364. 27/5125. 366. 24

Definitions:

• Exponential Expression: 5⁹5⁹= 5(5)(5)(5)(5)(5)(5)(5)(5)• Base: the repeated factor of an exponential

factor• Exponent: number of times that the base is

used as a factor– POWER

Review

• Evaluate the expression by substituting the number in for the variable

• X = -3 y = 4 z = -1

2x²y = _________

Answer: 2(-3)²(4) = 72

9 Z²x

9 (-1)²(-3)

9/(-3) = -3

• What does x³?

X³ = (x)(x)(x)

Product Rule for Exponents• If m and n are positive

integers, and b is a real number, then…..

• Example: 3³· 3⁴ = 3⁷Why?(3·3·3) · (3·3·3·3) = 3⁷

Examples:

1. 4³· 4 = 2. (-3)²· (-3)⁷ = 3. x³· x · x²=

4. 3x³ · 4x² = 5. (3y⁴)(-10x⁷)(4xy³) =

1. 4⁴2. (-3)⁹3. x⁶

4. (3 · 4) (x³ ·x²) = 12x⁵5. (3· -10 · 4)(y⁴ · y³)(x⁷ · x) = -120y⁷x⁸

Helpful Hint – p. 299

• Multiplication:5x² · 4x² = 20x⁴

6x³ · 7x² = 42x⁵

• Addition:5x² + 4x² = 9x²

6x³ + 7x² = Cannot simplify! Not

like terms!

Let’s think about it!

(x²)³ = (x²)(x²)(x²)= x⁶

Shortcut: Power Rule for Exponents

If m and n are positive integers, and b is a real number, then…….

Example:

(y⁴)² = y⁸

Practice:

1. (9⁶)⁸ = 2. (x⁹)⁷ =

• Think about it:• (2x⁵y⁴)³

Remember: (2x⁵y⁴)(2x⁵y⁴)(2x⁵y⁴)

(2 · 2 · 2)(x⁵ · x⁵· x⁵)(y⁴ · y⁴ · y⁴)

Short Cut: Power of a Product Rule

If n is a positive integer and a and b are real numbers, then…..

Examples:1). (3y)⁴ 2). (-2g²hj³)⁴

Power of a Quotient Rule• If m is a positive integer

and b and c are real numbers, then…..

Example:

Think of your own rule: Simplify each one

Quotient Rule for Exponents

• If m and n are positive integers, and b is a real number, then…..

Why are these two the same?

x⁴x⁴

55

Zero Exponent Rule

If a is a real number, then…

As long as a is not zero!

Practice

1. x⁰2. 7⁰3. (-3)⁰4. -3⁰5. x⁵y⁰

1. 12. 13. 14. -15. x⁵