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Popular >

simplify 81^{-3/4}

Solution

simplify

8 1^{- \frac{3}{4}}

Solution

\frac{1}{27}

+1

Decimal Notation

0.03703 \dots

Solution steps

8 1^{- \frac{3}{4}}

Factor the number:

81 = 3^{4}

= (3^{4})^{- \frac{3}{4}}

Apply exponent rule:

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

= 3^{4 (- \frac{3}{4})}

4 (- \frac{3}{4}) = - 3

= 3^{- 3}

Apply exponent rule:

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

3^{- 3} = \frac{1}{3 ^{3}}

= \frac{1}{3 ^{3}}

3^{3} = 27

= \frac{1}{27}

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Frequently Asked Questions (FAQ)

What is 81^{-3/4} ?
The solution to 81^{-3/4} is 1/27