2 Answers

Butterywombat · Answer 1 · 2021-06-21T16:59:03+0000

Answer:

$xy^{(2)/(9)}$ =
$x\sqrt[9]{y^2}$

Step-by-step explanation:

Given

$xy^{(2)/(9)}$

Required

Write an equivalent expression

$xy^{(2)/(9)}$

Split the expression

$x * y^{(2)/(9)}$

Further, simplify using the following law of indices:
$a^{ (m)/(n)} = a^{ m * (1)/(n)}$

$x * y^{(2)/(9)}$ becomes

$x * y^{2 * (1)/(9)}$

This in turn gives:

$x * (y^(2)) ^{* { (1)/(9)}}$

In indices:
$y^{(1)/(n)} = \sqrt[n] y$

$x * (y^(2)) ^{* { (1)/(9)}}$ becomes

$x * \sqrt[9]{ y^2}$

$x\sqrt[9]{y^2}$

Hence:

$xy^{(2)/(9)}$ =
$x\sqrt[9]{y^2}$

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