Question

Find the value of (4/25)^-1/2

Answer 1

The value of the given exponent is $\frac{5}{2}$

Given:

The exponent = $(\frac{4}{25})^{\frac{-1}{2}}$

To find:

The value of a given exponent

Solution:

$(\frac{4}{25})^{\frac{-1}{2}} = ?$

Using the identity of an exponent : $(\frac{m}{n})^{x} = \frac{m^{x}}{n^{x}}$

$(\frac{4}{25})^{\frac{-1}{2}} = \frac{(4)^{(\frac{-1}{2})}}{(25)^{(\frac{-1}{2})}}$

Using the identity of an exponent : $a^{-x} = \frac{1}{a^x}$

$=\frac{(25)^{(\frac{1}{2})}}{(4)^{(\frac{1}{2})}}\\=\frac{(25)^{(\frac{1}{2})}}{(4)^{(\frac{1}{2})}}\\=\frac{((5)^2)^{(\frac{1}{2})}}{((2)^2)^{(\frac{1}{2})}}$

Using the identity of an exponent: $(a^{n})^m=a^{m\times n}$

$=\frac{5^{(2\times \frac{1}{2})}}{2^{(2\times \frac{1}{2})}}\\=\frac{5^1}{2^1}\\=\frac{5}{2}$

The value of the given exponent is $\frac{5}{2}$.

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