which expression is equivalent to $(x^{27}y)^{\frac{1}{3}}$?\n$x^{3}(sqrt3{y})$\n$x^{9}(sqrt3{y})$\n$x^{27}(s…

which expression is equivalent to $(x^{27}y)^{\frac{1}{3}}$?\n$x^{3}(sqrt3{y})$\n$x^{9}(sqrt3{y})$\n$x^{27}(sqrt3{y})$\n$x^{24}(sqrt3{y})$

which expression is equivalent to $(x^{27}y)^{\frac{1}{3}}$?\n$x^{3}(sqrt3{y})$\n$x^{9}(sqrt3{y})$\n$x^{27}(sqrt3{y})$\n$x^{24}(sqrt3{y})$

Answer

Explanation:

Step1: Apply power - of - a - product rule

According to the rule ((ab)^n=a^n\times b^n), for ((x^{27}y)^{\frac{1}{3}}), we have ((x^{27}y)^{\frac{1}{3}}=x^{27\times\frac{1}{3}}y^{\frac{1}{3}}).

Step2: Calculate the exponent of (x)

Calculate (27\times\frac{1}{3}). Since (27\div3 = 9), then (x^{27\times\frac{1}{3}}=x^{9}). And (y^{\frac{1}{3}}=\sqrt[3]{y}). So ((x^{27}y)^{\frac{1}{3}}=x^{9}\sqrt[3]{y}).

Answer:

(x^{9}(\sqrt[3]{y})) (corresponding to the second option)