Question

which expression is equivalent to ^3 square root 216x^3 y^6 z^12 ?

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

Answer 1

Alternative 1 ) 6xy^2z^4
hope it helps

Answer 2

Answer:

Option A.

Step-by-step explanation:

The given expression is

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

We need to find the simplified form of the given expression.

It can be rewritten as

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

Using the properties of exponents, we get

$(6^3x^3y^6z^{12})^{\frac{1}{3}}$          $[\because \sqrt[n]{x}=x^{\frac{1}{n}}]$

$(6^3)^{\frac{1}{3}}(x^3)^{\frac{1}{3}}(y^6)^{\frac{1}{3}}(z^{12})^{\frac{1}{3}}$         $[\because (ab)^x=a^xb^x]$

$6^{\frac{3}{3}}x^{\frac{3}{3}}y^{\frac{6}{3}}z^{\frac{12}{3}}$         $[\because (x^m)^n=x^{mn}]$

$6^{1}x^{1}y^{2}z^{4}$  

$6xy^{2}z^{4}$  

Hence, the correct option is A.