How do you simplify ${(x^{- 4})}^{5}$ $(x^-4)^5$ and write it using only positive exponents?

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Answer 1 · 2017-02-11T07:05:01

$\frac{1}{x^{20}}$ $1/x^20$

Recall that:
(i) $x^{- m} = \frac{1}{x^{m}}$ $x^-m=1/x^m$ and
(ii) ${(x^{m})}^{n} = x^{m \times n}$ $(x^m)^n = x^(m xx n)$

${(x^{- 4})}^{5} = {(\frac{1}{x^{4}})}^{5}$ $(x^-4)^5 = (1/x^4)^5$ Applying (i) above

${(\frac{1}{x^{4}})}^{5} = \frac{1^{5}}{x^{4 \times 5}} = \frac{1}{x^{20}}$ $(1/x^4)^5 = 1^5/x^(4 xx 5) = 1/x^20$ Applying (ii) above

How do you simplify (x−4)5(x^-4)^5 and write it using only positive exponents?