Respuesta :

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:

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

Step-by-step explanation:

The given expression is [tex](x^{27}y)^{\frac{1}{3} }[/tex].

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

[tex](x^{27}y)^{\frac{1}{3} }=(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}[/tex]

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

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

Therefore Option B. is the answer.