Question

SIMPLIFY 8^1/3 * 16^1/4 divided by 32^1/5

Answer 1

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ANSWER:--------------

Do ,as the steps follows

8 divided by 1/3and multiplied by16th divided by 1/3

than,32={-1/3}

=[3√8×16×13×62]

=[3√2³×2⁴×2⅝{5}

=[2(12/3]

=[2⁴]

=[16]

hence proved.

hope it helps:--

T!—!ANS!!!

Answer 2

$\underline{\mathbf{\huge{Question}}}$

$\mathbf{ \frac{8 {}^{ \frac{1}{3} } \times 16 {}^{ \frac{1}{4} } }{32 {}^{ \frac{1}{5} } } }$

$\underline{\mathbf{\huge{Answer}}}$

As we know

${x}^{ \frac{a}{b} } = \sqrt[b]{x {}^{a} }$

Then,

${8}^{ \frac{1}{3} } = \sqrt[3]{8}$

Prime Factor of 8=2×2×2

So

$\sqrt[3]{8} = 2$

${16}^{ \frac{1}{4} } = \sqrt[4]{16}$

Prime Factor of 16=2×2×2×2

$\sqrt[4]{16} = 2$

${32}^{ \frac{1}{5} } = \sqrt[5]{32}$

Prime Factor of 32=2×2×2×2×2

$\sqrt[5]{32} = 2$

So ,

$\mathbf{ \frac{8 {}^{ \frac{1}{3} } \times 16 {}^{ \frac{1}{4} } }{32 {}^{ \frac{1}{5} } } } = \mathbf{\frac{2 \times 2}{2} } \\ \\ = \mathbf{ \frac{4}{2} } \\ \\ = \mathbf{2}$

$\boxed{\mathbf{\huge{Answer=2}}}$