Question

Which expression is equivalent to ? Assume .

Answer 1

Answer: $(x^{\dfrac{2}{7}})(y^{-\dfrac{3}{5}})$

Step-by-step explanation:

The given expression : $\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3} }$

Law of radicals :-

$\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}$

Law of exponent:

$\dfrac{1}{a^n}=a^{-n}$

Using the above law of radicals and law of exponent we have,

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

Answer 2

$\text{Use}\ \sqrt[n]{a^m}=a^{\frac{m}{n}}\ \text{and}\ a^{-1}=\dfac{1}{a}\\\\\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}=\left(x^{\frac{2}{7}\right)\left(\dfrac{1}{y^\frac{3}{5}}\right)=\left(x^{\frac{2}{7}}\right)\left(y^{-\frac{3}{5}}\right)$