# How do you evaluate the expression (2^3)^2/(2^-4 using the properties?

Apr 8, 2017

${2}^{10} = 1024$

#### Explanation:

To begin simplifying, we apply two of the laws of indices.

$\textcolor{red}{{\left({x}^{m}\right)}^{n} = {x}^{m \times n}} \text{ "and " } \textcolor{b l u e}{\frac{1}{x} ^ - m = {x}^{m}}$

$\frac{\textcolor{red}{{\left({2}^{3}\right)}^{2}}}{\textcolor{b l u e}{{2}^{-} 4}} = \textcolor{red}{{2}^{6}} \times \textcolor{b l u e}{{2}^{4}}$

Now apply the multiply law of indices (add the indices of like bases)

${2}^{m} \times {2}^{n} = {2}^{m + n}$

${2}^{6} \times {2}^{4} = {2}^{10}$

"Evaluate means to find the value of the expression, so we must give a number answer."

${2}^{10} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024$