Solve for: 5^7 * ((5^{-2})^4)/(5^2)

Expression: ${5}^{7} \times \frac{ {\left( {5}^{-2} \right)}^{4} }{ {5}^{2} }$

Simplify the expression by multiplying exponents

${5}^{7} \times \frac{ {5}^{-8} }{ {5}^{2} }$

Cancel out the common factor ${5}^{2}$

${5}^{5} \times {5}^{-8}$

Calculate the product

${5}^{-3}$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\frac{ 1 }{ {5}^{3} }$

Evaluate the power

$\begin{align*}&\frac{ 1 }{ 125 } \\&\begin{array} { l }0.008,& {5}^{-3}\end{array}\end{align*}$