5.1.5 Simplifying Exponents

5.1.5 • Simplifying Exponents

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.

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	$(\frac{a}{b})^{- n} = (\frac{b}{a})^{n}$

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

1.

Compare your answers:

Exponent Property Review