# How do you simplify (4x^5 (x^-1)^3)/((x^-2)^-2)?

Oct 1, 2016

$\frac{4 {x}^{5} {\left({x}^{- 1}\right)}^{3}}{{x}^{- 2}} ^ \left(- 2\right) = \frac{4}{x} ^ 2$

#### Explanation:

We will use the identities ${a}^{- m} = \frac{1}{a} ^ m$, ${\left({a}^{m}\right)}^{n} = {a}^{\left(m \times n\right)}$ and ${a}^{m} \cdot {a}^{n} = {a}^{\left(m + n\right)}$

Hence $\frac{4 {x}^{5} {\left({x}^{- 1}\right)}^{3}}{{x}^{- 2}} ^ \left(- 2\right)$

= (4x^5x^((-1)xx3))/(x^((-2)xx(-2))

= $\frac{4 {x}^{5} {x}^{- 3}}{{x}^{4}}$

= $\frac{4 {x}^{5} \times 1}{{x}^{3} \times {x}^{4}}$

= (4x^5)/(x^(3+4)

= $\frac{4 {x}^{5}}{x} ^ 7$

= $\frac{4}{x} ^ \left(7 - 5\right)$

= $\frac{4}{x} ^ 2$