One-Step Exponent Law Practice

EXPONENT LAWS

Let

$\,x\,$, $\,y\,$, $\,m\,$, and $\,n\,$ be real numbers, with the following exceptions:

a base and exponent cannot simultaneously be zero (since $\,0^0\,$ is undefined);
division by zero is not allowed;
for non-integer exponents (like $\,\frac12\,$ or $\,0.4\,$), assume that bases are positive.

Then,

$x^mx^n = x^{m+n}$	Verbalize: same base, things multiplied, add the exponents
$\displaystyle \frac{x^m}{x^n} = x^{m-n}$	Verbalize: same base, things divided, subtract the exponents
$(x^m)^n = x^{mn}$	Verbalize: something to a power, to a power; multiply the exponents
$(xy)^m = x^my^m$	Verbalize: product to a power; each factor gets raised to the power
$\displaystyle \left(\frac{x}{y}\right)^m = \frac{x^m}{y^m}$	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:

$\displaystyle x^2x^{-5} = x^p\,$ where $\,p = \text{?}$

Answer: $p = -3$

$\displaystyle \frac{x^5}{x^3} = x^p\,$ where $\,p = \text{?}$

Answer: $p = 2$

$\displaystyle (x^3)^2 = x^p\,$ where $\,p = \text{?}$

Answer: $p = 6$

$\displaystyle \frac{1}{x^7} = x^p$ where $\,p = \text{?}$

Answer: $p = -7$

$\displaystyle \frac{1}{x^{-7}} = x^p$ 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

(an even number, please)