1 Answer

Jess Patton · Answer 1 · 2021-11-04T16:03:55+0000

Answer:

$2xy\sqrt[3]{2x^2z}$ and
$2xy(2x^2z)^{(1)/(3)}$ .

Explanation:

The given radical expression is

$\sqrt[3]{16x^5y^3z}$

We have to simplify the above expression.

The above expression can be written as

$\sqrt[3]{(2* 8)(x^(3+2))y^3z}$

$\sqrt[3]{(2* 2^3)(x^3* x^2)y^3z}$
$[\because a^(m+n)=a^ma^n]$

$\sqrt[3]{(2^3x^3y^3)(2x^2z)}$

$\sqrt[3]{(2xy)^3}\sqrt[3]{2x^2z}$
$[\because (ab)^m=a^mb^m]$

$2xy\sqrt[3]{2x^2z}$
$[\because \sqrt[n]{x^n}=x]$

It can be written as exponent form.

$2xy(2x^2z)^{(1)/(3)}$
$[\because \sqrt[n]{a}=a^{(1)/(n)}]$

Therefore, the required expressions are
$2xy\sqrt[3]{2x^2z}$ and
$2xy(2x^2z)^{(1)/(3)}$ .

Please log in or register to add a comment.