Question

Simplify the radical expression.

4 sqrt 625x^12y^8

Answer 1

Answer:

$\sqrt[4]{625x^{12}y^8} = 5 {x^3} {y^2}$

Step-by-step explanation:

Given

$\sqrt[4]{625x^{12}y^8}$

Required

Simplify

We start by splitting the roots

$\sqrt[4]{625x^{12}y^8} = \sqrt[4]{625}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}$

Express 625 as exponents

$\sqrt[4]{625x^{12}y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}$

From laws of indices

$\sqrt[n]{a^m} = a^{\frac{m}{n}}$

So,

$\sqrt[4]{625x^{12}y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^{12}} * \sqrt[4]{y^8}$ becomes

$\sqrt[4]{625x^{12}y^8} = {5^\frac{4}{4}} * {x^\frac{12}{4}} * {y^\frac{8}{4}}$

$\sqrt[4]{625x^{12}y^8} = 5 * {x^3} * {y^2}$

$\sqrt[4]{625x^{12}y^8} = 5 {x^3} {y^2}$