Question

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

Answer 1

Answer:

$\large\boxed{\left(x^{27}y\right)^\frac{1}{3}=x^9y^\frac{1}{3}=x^9\sqrt[3]{y}}$

Step-by-step explanation:

$\left(x^{27}y\right)^\frac{1}{3}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(x^{27}\right)^\frac{1}{3}y^\frac{1}{3}=x^{(27)\left(\frac{1}{3}\right)}y^\frac{1}{3}=x^9y^\frac{1}{3}\\\\\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=x^9\sqrt[3]{y}$

Answer 2

Answer:

The equivalent form of the given expression is  $x^{9}\times\sqrt[3]{y}$                              

Step-by-step explanation:

Given : Expression $(x^{27}y)^\frac{1}{3}$

To find : The expression is equivalent to?

Solution :

Step 1 - Write the expression

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

Step 2 - Separating the power using $(xy)^a=x^a\times y^a$

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

Step 3 - Solving the power, $(x^a)^b=x^{a\times b}$

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

Step 4 - Simplifying

$=x^{9}\times\sqrt[3]{y}$           

So, The equivalent form of the given expression is $x^{9}\times\sqrt[3]{y}$