If $x^{\frac{3}{4}} = 27$ $x^(3/4) = 27$ , what is the value of x?

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If $x^{\frac{3}{4}} = 27$ $x^(3/4) = 27$ , what is the value of x?

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Answer 1 · 2015-09-05T09:15:22

$x = 81$ $x = 81$

Explanation:

Use $x^{a b} = {(x^{a})}^{b}$ $x^(ab) = (x^a)^b$ as follows:

$x = x^{1} = x^{\frac{3}{4} \cdot \frac{4}{3}} = {(x^{\frac{3}{4}})}^{\frac{4}{3}} = 27^{\frac{4}{3}}$ $x = x^1 = x^(3/4*4/3) = (x^(3/4))^(4/3) = 27^(4/3)$

$= {(3^{3})}^{\frac{4}{3}} = 3^{3 \cdot \frac{4}{3}} = 3^{4} = 81$ $= (3^3)^(4/3) = 3^(3*4/3) = 3^4 = 81$

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If $x^{\frac{3}{4}} = 27$ $x^(3/4) = 27$ , what is the value of x?

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Explanation:

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