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Popular >

simplify 1000^{(-2)/3}

Solution

simplify

100 0^{\frac{- 2}{3}}

Solution

\frac{1}{100}

+1

Solution steps

100 0^{\frac{- 2}{3}}

Factor the number:

1000 = 1 0^{3}

= (1 0^{3})^{\frac{- 2}{3}}

Apply exponent rule:

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

= 1 0^{3 \cdot \frac{- 2}{3}}

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

= 1 0^{- 2}

Apply exponent rule:

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

1 0^{- 2} = \frac{1}{1 0 ^{2}}

= \frac{1}{1 0 ^{2}}

1 0^{2} = 100

= \frac{1}{100}

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3 \cdot 1 0^{2} = 9 \cdot 1 0^{9} (\frac{x ^{2}}{( 0.003 ) ^{2}})

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Frequently Asked Questions (FAQ)

What is 1000^{(-2)/3} ?
The solution to 1000^{(-2)/3} is 1/100