How do you simplify $\frac{4 x^{5} {(x^{- 1})}^{3}}{{(x^{- 2})}^{- 2}}$ $(4x^5 (x^-1)^3)/((x^-2)^-2)$ ?

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How do you simplify $\frac{4 x^{5} {(x^{- 1})}^{3}}{{(x^{- 2})}^{- 2}}$ $(4x^5 (x^-1)^3)/((x^-2)^-2)$ ?

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Answer 1 · 2016-10-01T14:32:38

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

Explanation:

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

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

= $\frac{4 x^{5} x^{(- 1) \times 3}}{x^{(- 2) \times (- 2)}}$ $(4x^5x^((-1)xx3))/(x^((-2)xx(-2))$

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

= $\frac{4 x^{5} \times 1}{x^{3} \times x^{4}}$ $(4x^5xx1)/(x^3xx x^4)$

= $\frac{4 x^{5}}{x^{3 + 4}}$ $(4x^5)/(x^(3+4)$

= $\frac{4 x^{5}}{x^{7}}$ $(4x^5)/x^7$

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

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

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How do you simplify $\frac{4 x^{5} {(x^{- 1})}^{3}}{{(x^{- 2})}^{- 2}}$ $(4x^5 (x^-1)^3)/((x^-2)^-2)$ ?

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How do you simplify $\frac{4 x^{5} {(x^{- 1})}^{3}}{{(x^{- 2})}^{- 2}}$ $(4x^5 (x^-1)^3)/((x^-2)^-2)$ ?