Mathematics: Which expression is equivalent to (x^27y)^1/3? a) x^3 (3√y) b) x^9 (3√y) c) x^27 (3√y) d) x^24 (3√y)

Which expression is equivalent to (x^27y)^1/3? a)

neariah24

06.01.2022

Option B). $x^{9}.(\sqrt[3]{y} )$ .

Step-by-step explanation:

The given expression is $(x^{27}y)^{\frac{1}{3} }$ .

We have to further simplify so that we can get the answer as shown in the options.

$(x^{27}y)^{\frac{1}{3} }=(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}$

[ As $(x^{a}.y^{b})^{m}=(x^{a})^{m}.(y^{b})^{m}$ ]

Now ( $(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}=(x^{\frac{27}{3} }).(y^{\frac{1}{3} } )=x^{9}.(\sqrt[3]{y} )$

Therefore Option B. is the answer.

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monkeys450

13.09.2020

Cool

Explanation:

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