Question

The expression ${\left({\left(\right(625{)}^{\frac{1}{2}})}^{-\frac{1}{4}}\right)}^2$, when simplified reduces to

• A. $5$
• B. $\frac{1}{5}$
• C. $25$
• D. $\frac{1}{25}$

Answer 1

The correct option is B $\frac{1}{5}$

Given:

$E={\left[{\left({\left(625\right)}^{\frac{1}{2}}\right)}^{\frac{-1}{4}}\right]}^2$

$\Rightarrow E={625}^k$

where, $k=\frac{1}{2}\times \left(\frac{-1}{4}\right)\times 2$

$\because {\left(a^b\right)}^c=(a{)}^{bc}$

$\therefore k=-\frac{1}{4}$ ...... (Power rule)

Now,

$E={625}^{\left(\frac{-1}{4}\right)}$

$={\left(5^4\right)}^{\left(\frac{-1}{4}\right)}$

Using power rule

$E=5^{-1}=\frac{1}{5}$ $\because a^{-m}=\frac{1}{a^m}$

Hence, option B.