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

Jun 16, 2016

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

#### Explanation:

Use the power law of indices.. "Multiply the indices".

$\frac{4 {x}^{5} \left({x}^{-} 3\right)}{{x}^{4}} \text{ now simplify}$

$\frac{4 {x}^{5} \times {x}^{-} 3}{x} ^ 4 = \frac{4 {x}^{2}}{x} ^ 4$

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

OR, you could deal with the negative index first by moving it to the denominator so the index is positive.

$\frac{4 {x}^{5}}{{x}^{4} \times {x}^{3}} = \frac{4 {x}^{5}}{x} ^ 7$

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

Which method you use is entirely your choice, one is not better than the other.

Jun 16, 2016

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

#### Explanation:

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

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

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

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

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

= $4 {x}^{- 2}$

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