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Popular >

simplify (81^{1/4})^{-2}

Solution

simplify

(8 1^{\frac{1}{4}})^{- 2}

Solution

\frac{1}{9}

+1

Solution steps

(8 1^{\frac{1}{4}})^{- 2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 8 1^{\frac{1}{4} (- 2)}

\frac{1}{4} (- 2) = - \frac{1}{2}

= 8 1^{- \frac{1}{2}}

Factor the number:

81 = 9^{2}

= (9^{2})^{- \frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 9^{2 (- \frac{1}{2})}

2 (- \frac{1}{2}) = - 1

= 9^{- 1}

Apply exponent rule:

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

9^{- 1} = \frac{1}{9}

= \frac{1}{9}

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Frequently Asked Questions (FAQ)

What is (81^{1/4})^{-2} ?
The solution to (81^{1/4})^{-2} is 1/9