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Popular >

simplify 144^{-3/2}

Solution

simplify

14 4^{- \frac{3}{2}}

Solution

\frac{1}{1728}

+1

Decimal Notation

0.00057 \dots

Solution steps

14 4^{- \frac{3}{2}}

Factor the number:

144 = 1 2^{2}

= (1 2^{2})^{- \frac{3}{2}}

Apply exponent rule:

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

= 1 2^{2 (- \frac{3}{2})}

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

= 1 2^{- 3}

Apply exponent rule:

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

1 2^{- 3} = \frac{1}{1 2 ^{3}}

= \frac{1}{1 2 ^{3}}

1 2^{3} = 1728

= \frac{1}{1728}

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Frequently Asked Questions (FAQ)

What is 144^{-3/2} ?
The solution to 144^{-3/2} is 1/1728