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Popular >

simplify 64^{(-3)/2}

Solution

simplify

6 4^{\frac{- 3}{2}}

Solution

\frac{1}{512}

+1

Decimal Notation

0.001953125

Solution steps

6 4^{\frac{- 3}{2}}

Factor the number:

64 = 8^{2}

= (8^{2})^{\frac{- 3}{2}}

Apply exponent rule:

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

= 8^{2 \cdot \frac{- 3}{2}}

2 \cdot \frac{- 3}{2} = - 3

= 8^{- 3}

Apply exponent rule:

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

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

= \frac{1}{8 ^{3}}

8^{3} = 512

= \frac{1}{512}

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Frequently Asked Questions (FAQ)

What is 64^{(-3)/2} ?
The solution to 64^{(-3)/2} is 1/512