# How do you rewrite the expression (–2x^5)^5(4x^5)^-1 with positive exponents?

Feb 2, 2015

The answer is: $- 8 {x}^{20}$.

Using the properties of the powers:

${\left(- 2 {x}^{5}\right)}^{5} {\left(4 {x}^{5}\right)}^{-} 1 = {\left(- 2\right)}^{5} {\left({x}^{5}\right)}^{5} {\left({2}^{2}\right)}^{-} 1 {\left({x}^{5}\right)}^{-} 1 = - {2}^{5} {x}^{25} \cdot {2}^{-} 2 {x}^{-} 5 = - {2}^{5 - 2} {x}^{25 - 5} = - {2}^{3} {x}^{20} = - 8 {x}^{20}$.

The properties used are:

${a}^{n} \cdot {a}^{m} = {a}^{n + m}$, and

${\left({a}^{n}\right)}^{m} = {a}^{n \cdot m}$.