Question

$\sqrt[4]{ {x}^{6 {y}^{8 } } } \div \sqrt[3]{x {}^{6} } {y}^{8}$
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Answer 1

★ Given -:

$\sqrt[4]{{x^{6 {y} ^8}}} \div \sqrt[3]{x {}^{ 6 }} {y}^{8}$

★ Solution -:

We know that ,

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

⁴√x⁶y⁸ =

⁴√x⁶ × ⁴√y⁸

$= (x^\cancel{6})^{\frac{1}{\cancel{4}}} \times. (y^\cancel{8})^{\frac{1}{\cancel{4}}}$

$= x^{\frac{3}{2}} y^2$

³√x⁶ y⁸ =

³√x ⁶ * ³√y⁸

In the same way ,

³√x⁶y⁸ =

$x^2 y^{\frac{8}{3}}$

by putting the simplified values in the given equation ..

$x^{\frac{3}{2}} y^2 \div x^2 y^{\frac{8}{3}}$

We know that ,

$a^m \div a^n = a^{m-n}$

by using the law ,

$= \dfrac{x^{3}{2}}}{x^2} \times \dfrac{y^2}{y^{\frac{8}{3}}}$

$= x^{\frac{3}{2} - 2} \times y^{2 - \frac{8}{3}}$

$\purple{ Answer => x^{- \frac{1}{2}} y^{- \frac{2}{3}} }$