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

1 Answer
Feb 11, 2017

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

Explanation:

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

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

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