Solve:
$x^{\frac{1}{2}}$; by $x^{\frac{5}{2}}$

Given: $x^{\frac{1}{2}}$  and  $x^{\frac{5}{2}}$

To find: Here in this case we have to find the value of $x^{\frac{1}{2}}$ by $x^{\frac{5}{2}}$.

Solution:

$x^{\frac{1}{2}}$  by  $x^{\frac{5}{2}}$

$=\ \frac{x^{\left(\frac{1}{2}\right)}}{x^{\left(\frac{5}{2}\right)}}$

$=\ x^{\left(\frac{1}{2}\right)} \ \times \ x^{\left( -\frac{5}{2}\right)}$

Using property a^m $\times$ aⁿ = a^{(m + n)}

$=\ x^{\left(\frac{1}{2} \ -\ \frac{5}{2}\right)}$

$=\ x^{\left( -\ \frac{4}{2}\right)}$

$=\ x^{( -\ 2)}$

$=\mathbf{\ \frac{1}{x^{2}}}$

So, the value of the given expression is $\frac{1}{x^{2}}$.

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Updated on: 10-Oct-2022

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