Mathematics: Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (x4y8)2/3

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Simplify the expression by using the properties

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30.01.2022

Mathematics

$x^\frac{8}{3} y^\frac{16}{3}$

Step-by-step explanation:

Given the expression $(x^4y^8)^\frac{2}{3}$ , to simplify the expression using the rational exponents;

Applying one of the law of indices to simplify the expression;

$(a^m)^n = a^{mn}$

$(x^4y^8)^\frac{2}{3}\\\\= (x^4)^\frac{2}{3} * (y^8)^\frac{2}{3}\\\\= x^{4*\frac{2}{3} } * y^{8*\frac{2}{3} }\\\\= x^\frac{8}{3} * y^\frac{16}{3}\\ \\The \ final \ expression \ will \ be \ x^\frac{8}{3} y^\frac{16}{3}$

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Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (x4y8)2/3

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