Mathematics: 20 pts and brainiest for correct

20 pts and brainiest for correct - id2010624870, jshhs

cheyennegolden6621

09.06.2022

Option A.

Step-by-step explanation:

The given expression is

$\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}$

where, $y\neq 0$ .

We need to find the expression which is equivalent to the given expression.

The given expression can be rewritten as

$\dfrac{(x^2)^{\frac{1}{7}}}{(y^3)^{\frac{1}{5}}}$ $[\because \sqrt[n]{x}=x^{\frac{1}{n}}]$

$\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}$ $[\because (a^m)^n=a^{mn}]$

$x^{\frac{2}{7}}y^{-\frac{3}{5}}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

Therefore, the correct option is A.

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