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Popular >

simplify 9^{-3/2}

Solution

simplify

9^{- \frac{3}{2}}

Solution

\frac{1}{27}

+1

Decimal Notation

0.03703 \dots

Solution steps

9^{- \frac{3}{2}}

Factor the number:

9 = 3^{2}

= (3^{2})^{- \frac{3}{2}}

Apply exponent rule:

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

= 3^{2 (- \frac{3}{2})}

2 (- \frac{3}{2}) = - 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 9^{-3/2} ?
The solution to 9^{-3/2} is 1/27