What is x^{-4}*(x^{-4})^4 ?

The solution to x^{-4}*(x^{-4})^4 is 1/(x^{20)}

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simplify x^{-4}*(x^{-4})^4

simplify

x^{- 4} \cdot (x^{- 4})^{4}

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

Solution steps

x^{- 4} (x^{- 4})^{4}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- 4} = \frac{1}{x ^{4}}

= \frac{1}{x ^{4}} (x^{- 4})^{4}

Simplify

(x^{- 4})^{4} : \frac{1}{x ^{16}}

= \frac{1}{x ^{4}} \cdot \frac{1}{x ^{16}}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{x ^{4} x ^{16}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{x ^{4} x ^{16}}

Simplify

x^{4} x^{16} : x^{20}

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

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