Question

Smplify the radical expression. How many different ways can you write your answer?

Answer 1

Answer:

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

Step-by-step 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

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

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

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

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

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

It can be written as exponent form.

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

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