What is [(1000000x^6)^{-1/3}]^{-1/2} ?

The solution to [(1000000x^6)^{-1/3}]^{-1/2} is 10x

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simplify [(1000000x^6)^{-1/3}]^{-1/2}

simplify

[(1000000 x^{6})^{- \frac{1}{3}}]^{- \frac{1}{2}}

10 x

Solution steps

((1000000 x^{6})^{- \frac{1}{3}})^{- \frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (1000000 x^{6})^{- \frac{1}{3} (- \frac{1}{2})}

- \frac{1}{3} (- \frac{1}{2}) = \frac{1}{6}

= (1000000 x^{6})^{\frac{1}{6}}

Apply exponent rule:

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

(1000000 x^{6})^{\frac{1}{6}} = 100000 0^{\frac{1}{6}} (x^{6})^{\frac{1}{6}}

= 100000 0^{\frac{1}{6}} (x^{6})^{\frac{1}{6}}

100000 0^{\frac{1}{6}} = 10

= 10 (x^{6})^{\frac{1}{6}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{6})^{\frac{1}{6}} = x^{6 \cdot \frac{1}{6}}

= 10 x^{6 \cdot \frac{1}{6}}

6 \cdot \frac{1}{6} = 1

= 10 x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= 10 x

\frac{5 π}{4} + π

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\frac{x}{72 - x} \leq \frac{1}{x}

What is [(1000000x^6)^{-1/3}]^{-1/2} ?
The solution to [(1000000x^6)^{-1/3}]^{-1/2} is 10x