5.1.5 Simplifying Exponents

Algebra 15.1.5 Simplifying Exponents

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Cool Down

Complete the table using all of the exponent properties you learned in the lesson.

Expression	Simplified Result
$j^{5} \cdot j^{3}$
$\frac{h^{7}}{h^{3}}$
$(- a b)^{0}$
$\frac{1}{s^{- 4}}$
$(\frac{m}{n})^{- 4}$
$(p^{5})^{2}$
$(3 s^{3} t^{2})^{3}$
$(\frac{b}{d})^{- 2}$

Exponent Property Review

Compare your answers:

Expression	Simplified Result
$j^{5} \cdot j^{3}$	$j^{8}$
$\frac{h^{7}}{h^{3}}$	$h^{4}$
$(- a b)^{0}$	$1$
$\frac{1}{s^{- 4}}$	$s^{4}$
$(\frac{m}{n})^{- 4}$	$\frac{n^{4}}{m^{4}}$
$(p^{5})^{2}$	$p^{10}$
$(3 s^{3} t^{2})^{3}$	$3^{3} s^{9} t^{6} = 27 s^{9} t^{6}$
$(\frac{b}{d})^{- 2}$	$\frac{d^{2}}{b^{2}}$

Exponent Property Review

Take some time to review each of the exponential properties you learned in the lesson. Look at each property and be sure you know when to use it.

Summary of Exponent Properties

If $a$ and $b$ are real numbers and $m$ and $n$ are integers, then

Property	Description
Product Property	$a^{m} \cdot a^{n} = a^{m + n}$
Power Property	$(a^{m})^{n} = a^{m \cdot n}$
Product to a Power	$(a b)^{m} = a^{m} b^{m}$
Quotient Property	$\frac{a^{m}}{a^{n}} = a^{m - n}$ , $a \neq 0$
Zero Exponent Property	$a^{0} = 1$ , $a \neq 0$
Quotient to a Power Property	$(\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}}$ , $b \neq 0$
Properties of Negative Exponents	$a^{- n} = \frac{1}{a^{n}}$ and $\frac{1}{a^{- n}} = a^{n}$
Quotient to a Negative Exponent	$(\frac{a}{b})^{- n} = (\frac{b}{a})^{n}$

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