Question

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

Answer 1

Remember that (xᵃ. yᵇ)ⁿ = xᵃⁿ.yᵇⁿ

(x²⁷.y)¹/³ = x⁽²⁷ˣ¹/³⁾. y¹/³

x⁽²⁷ˣ¹/³⁾. y¹/³ =x⁸. y¹/³ = x⁹. ∛y. NONE OF THE ANSWERS, UNLESS YOU HAVE OMITTED SOMETHING, JUST AS 27 IS THE EXPONENT OF X AND ALSO ANOTHER 27 THAT MULTIPLIES Y??, In this case, it will be b

Answer 2

Answer:

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.