Question

Simplify $[\frac{15^\frac{1}{4} }{3^\frac{1}{2} }]$

Answer 1

To Find :

The value of :

$\tt{ \frac{ {15}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{2} } } }$

Solution :

$\large\tt{ \frac{ {15}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{2} } } }$

$\large{\tt{ \implies \frac{ {3}^{ \frac{1}{4} } \times {5}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{2} } } }}$

$\large{\tt{ \implies \frac{ {3}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{2} } } \times {5}^{ \frac{1}{4} } } }$

Using the identity:

A²÷A³ = A²-³ , we get

$\large\tt{ \implies {3}^{ \frac{1}{4} - \frac{1}{2} } \times {5}^{ \frac{1}{4} } }$

$\implies \large\tt{ {3}^{ \frac{ - 1}{4} } \times {5}^{ \frac{1}{4} } }$

$\large\tt{ \implies {( {3}^{ - 1} \times 5)}^{ \frac{1}{4} }}$

$\large\implies \tt{ {( \frac{5}{3}) }^{ \frac{1}{4} } }$

Hence,

$\large{\implies \tt{ \frac{ {15}^{ \frac{1}{4} } }{ {3}^{ \frac{1}{2} } } = {( \frac{5}{3} )}^{ \frac{1}{4} } }}$

Hence, This is your solution.