# How do you simplify the expression (7c^7d^2)^-2 using the properties?

Mar 19, 2017

See the entire simplification process below:

#### Explanation:

First, use these two rules for exponents to remove the outer exponent from the expression:

$a = {a}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left(7 {c}^{7} {d}^{2}\right)}^{-} 2 = {\left({7}^{\textcolor{red}{1}} {c}^{\textcolor{red}{7}} {d}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{- 2}} = {7}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 2}} {c}^{\textcolor{red}{7} \times \textcolor{b l u e}{- 2}} {d}^{\textcolor{red}{2} \times \textcolor{b l u e}{- 2}} =$

${7}^{-} 2 {c}^{-} 14 {d}^{-} 4$

Now, use this rule for exponents to eliminate the negative exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${7}^{\textcolor{red}{- 2}} {c}^{\textcolor{red}{- 14}} {d}^{\textcolor{red}{- 4}} = \frac{1}{{7}^{\textcolor{red}{- - 2}} {c}^{\textcolor{red}{- - 14}} {d}^{\textcolor{red}{- - 4}}} = \frac{1}{{7}^{2} {c}^{14} {d}^{4}} = \frac{1}{49 {c}^{14} {d}^{4}}$