ONE-STEP EXPONENT LAW PRACTICE
EXPONENT LAWS
Let [beautiful math coming... please be patient] $\,x\,$, $\,y\,$, $\,m\,$, and $\,n\,$ be real numbers, with the following exceptions:
  • a base and exponent cannot simultaneously be zero (since [beautiful math coming... please be patient] $\,0^0\,$ is undefined);
  • division by zero is not allowed;
  • for non-integer exponents (like [beautiful math coming... please be patient] $\,\frac12\,$ or $\,0.4\,$), assume that bases are positive.
Then,
[beautiful math coming... please be patient] $x^mx^n = x^{m+n}$ Verbalize: same base, things multiplied, add the exponents
[beautiful math coming... please be patient] $\displaystyle \frac{x^m}{x^n} = x^{m-n}$ Verbalize: same base, things divided, subtract the exponents
[beautiful math coming... please be patient] $(x^m)^n = x^{mn}$ Verbalize: something to a power, to a power; multiply the exponents
[beautiful math coming... please be patient] $(xy)^m = x^my^m$ Verbalize: product to a power; each factor gets raised to the power
[beautiful math coming... please be patient] $\displaystyle \left(\frac{x}{y}\right)^m = \frac{x^m}{y^m}$ Verbalize: fraction to a power; both numerator and denominator get raised to the power

In this exercise you will practice with the exponent laws, all mixed-up.

EXAMPLES:
[beautiful math coming... please be patient] $\displaystyle x^2x^{-5} = x^p\,$   where   $\,p = \text{?}$
Answer: $p = -3$
[beautiful math coming... please be patient] $\displaystyle \frac{x^5}{x^3} = x^p\,$   where   $\,p = \text{?}$
Answer: $p = 2$
[beautiful math coming... please be patient] $\displaystyle (x^3)^2 = x^p\,$   where   $\,p = \text{?}$
Answer: $p = 6$
[beautiful math coming... please be patient] $\displaystyle \frac{1}{x^7} = x^p$   where   $\,p = \text{?}$
Answer: $p = -7$
[beautiful math coming... please be patient] $\displaystyle \frac{1}{x^{-7}} = x^p$ where $\,p = \text{?}$
Answer: $p = 7$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Multi-Step Exponent Law Practice

 
 
Simplify:
    
(an even number, please)