Question

Which expression is equivalent to 3sqt 216x^3y^6z^12

6xy^2z^4
18xy^3z^6
36xy^2z^4
72xy^3z^6

Answer 1

The equivalent expression of $\sqrt[3]{216x^3y^6z^{12}}$ is $6xy^2z^4$

Answer 2

Answer:

Option 1

$\sqrt[3]{216x^3y^6z^{12}}=6xy^2z^4$

Step-by-step explanation:

Given : Expression $\sqrt[3]{216x^3y^6z^{12}}$

To find : Which expression is equivalent to given expression?

Solution :

The given expression is

$\sqrt[3]{216x^3y^6z^{12}}$

We can write it as,

$=(216x^3y^6z^{12})^{\frac{1}{3}}$

Applying power rule, $(x^a)^b=x^{a\times b}$

$=(216)^\frac{1}{3}(x^3)^\frac{1}{3}(y^6)^\frac{1}{3}(z^{12})^{\frac{1}{3}}$

$=(6^3)^\frac{1}{3}(x^3)^\frac{1}{3}(y^6)^\frac{1}{3}(z^{12})^{\frac{1}{3}}$

$=6xy^2z^4$

Therefore, Option 1 is correct.

$\sqrt[3]{216x^3y^6z^{12}}=6xy^2z^4$