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Popular >

simplify 36^{(-3)/2}

Solution

simplify

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

Solution

\frac{1}{216}

+1

Decimal Notation

0.00462 \dots

Solution steps

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

Factor the number:

36 = 6^{2}

= (6^{2})^{\frac{- 3}{2}}

Apply exponent rule:

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

= 6^{2 \cdot \frac{- 3}{2}}

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

= 6^{- 3}

Apply exponent rule:

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

6^{- 3} = \frac{1}{6 ^{3}}

= \frac{1}{6 ^{3}}

6^{3} = 216

= \frac{1}{216}

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Frequently Asked Questions (FAQ)

What is 36^{(-3)/2} ?
The solution to 36^{(-3)/2} is 1/216