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Popular >

simplify-(25^{-3/2})

Solution

simplify

- (2 5^{- \frac{3}{2}})

Solution

- \frac{1}{125}

+1

Solution steps

- (2 5^{- \frac{3}{2}})

Apply rule:

- (a) = - a

- (2 5^{- \frac{3}{2}}) = - 2 5^{- \frac{3}{2}}

= - 2 5^{- \frac{3}{2}}

Factor the number:

25 = 5^{2}

= - (5^{2})^{- \frac{3}{2}}

Apply exponent rule:

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

= - 5^{2 (- \frac{3}{2})}

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

= - 5^{- 3}

Apply exponent rule:

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

5^{- 3} = \frac{1}{5 ^{3}}

= - \frac{1}{5 ^{3}}

5^{3} = 125

= - \frac{1}{125}

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Frequently Asked Questions (FAQ)

What is simplify-(25^{-3/2}) ?
The solution to simplify-(25^{-3/2}) is -1/125