3-2 Zero and Negative Exponents

3-2 Zero and Negative Exponents

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Zero Exponent

• As our exponent increases, we MULTIPLY by the base one fore time

• So, every time your exponent decreases, we DIVIDE by the base.

• When the exponent decreases from 1 to zero, we divide the base by itself and end up with 1

Zero Exponent Rule

Any non zero base with a zero exponent is equal to 1

Multiple Choice

Any number written to the 0 power is always 1

Example: 8⁰=1

• True

• False

Multiple Choice

x⁰

• 0

• 1

• x

• 12

Multiple Choice

Simplify (-4x)⁰

• -4

• -4x

• -1

• 1

• 0

Multiple Choice

Simplify -4x⁰

• -4

• -4x

• -1

• 1

• 0

Multiple Choice

(2a³b ∙ ba³)⁰

• 1

• 2ab

• 0

• 6ba

Multiple Choice

Which is greater, 2654⁰ or 5⁰?

• 2654⁰

• 5⁰

• They are the same

• This cannot be determined.

Negative Exponents

Negative Exponent Rule

Negative exponents can be written as the reciprocal fraction with a postive exponent

Negative Exponent Rule

Multiple Choice

Simplify x^-7

• -7

• -7x

• 
  

  $\frac{1}{x^7}$

• $-\frac{1}{x^7}$
  

Multiple Choice

Make this negative exponent positive.

9^-3

• 9³

• $\frac{1}{9^{-3}}$

  
  

• $\frac{1}{9^3}$
  

• 729

Multiple Choice

Rewrite using positive exponents.

3x⁻²

• $\frac{3}{x^2}$

• $\frac{1}{3^2}$

• $\frac{x^2}{3}$
  

• -3x²

Multiple Choice

Rewrite using positive exponents

 $\frac{1}{12^{-4}}$  

•  $\frac{1}{12^4}$  
  

•  $12^{-4}$  
  

•  $\frac{1}{20,736}$  

•  $12^4$