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Popular >

simplify 125^{(-2)/3}

Solution

simplify

12 5^{\frac{- 2}{3}}

Solution

\frac{1}{25}

+1

Solution steps

12 5^{\frac{- 2}{3}}

Factor the number:

125 = 5^{3}

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

Apply exponent rule:

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

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

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

= 5^{- 2}

Apply exponent rule:

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

5^{- 2} = \frac{1}{5 ^{2}}

= \frac{1}{5 ^{2}}

5^{2} = 25

= \frac{1}{25}

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Frequently Asked Questions (FAQ)

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