EXPONENT LAWS
Let
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$\,x\,$, $\,y\,$, $\,m\,$, and $\,n\,$
be real numbers,
with the following exceptions:
 a base and exponent cannot simultaneously be zero
(since
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$\,0^0\,$ is undefined);
 division by zero is not allowed;
 for noninteger exponents (like
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$\,\frac12\,$ or $\,0.4\,$),
assume that bases are positive.
Then,
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$x^mx^n = x^{m+n}$

Verbalize: same base, things multiplied, add the exponents

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$\displaystyle \frac{x^m}{x^n} = x^{mn}$

Verbalize: same base, things divided, subtract the exponents

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$(x^m)^n = x^{mn}$

Verbalize: something to a power, to a power; multiply the exponents

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$(xy)^m = x^my^m$

Verbalize: product to a power; each factor gets raised to the power

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$\displaystyle \left(\frac{x}{y}\right)^m = \frac{x^m}{y^m}$

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 mixedup.
EXAMPLES:
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$\displaystyle
x^2x^{5} = x^p\,$ where $\,p = \text{?}$
Answer:
$p = 3$
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$\displaystyle
\frac{x^5}{x^3} = x^p\,$ where $\,p = \text{?}$
Answer:
$p = 2$
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$\displaystyle
(x^3)^2 = x^p\,$ where $\,p = \text{?}$
Answer:
$p = 6$
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$\displaystyle
\frac{1}{x^7} = x^p$ where $\,p = \text{?}$
Answer:
$p = 7$
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$\displaystyle
\frac{1}{x^{7}} = x^p$ 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:
MultiStep Exponent Law Practice