What is [(1000000000a^9)^{-1/3}]^{-1/3} ?

The solution to [(1000000000a^9)^{-1/3}]^{-1/3} is 1000000000^{1/9}a

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simplify [(1000000000a^9)^{-1/3}]^{-1/3}

simplify

[(1000000000 a^{9})^{- \frac{1}{3}}]^{- \frac{1}{3}}

100000000 0^{\frac{1}{9}} a

Solution steps

((1000000000 a^{9})^{- \frac{1}{3}})^{- \frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (1000000000 a^{9})^{- \frac{1}{3} (- \frac{1}{3})}

- \frac{1}{3} (- \frac{1}{3}) = \frac{1}{9}

= (1000000000 a^{9})^{\frac{1}{9}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(1000000000 a^{9})^{\frac{1}{9}} = 100000000 0^{\frac{1}{9}} (a^{9})^{\frac{1}{9}}

= 100000000 0^{\frac{1}{9}} (a^{9})^{\frac{1}{9}}

Simplify

(a^{9})^{\frac{1}{9}} : a

= 100000000 0^{\frac{1}{9}} a

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What is [(1000000000a^9)^{-1/3}]^{-1/3} ?
The solution to [(1000000000a^9)^{-1/3}]^{-1/3} is 1000000000^{1/9}a