Question
Solved $$\root 4 \of {{{\left( {625} \right)}^3}} = ?$$
Answer: Option C
$$\eqalign{
& {\text{Given,}} \cr
& = \root 4 \of {{{\left( {625} \right)}^3}} \cr
& = {\left( {625} \right)^{\frac{3}{4}}} \cr
& = {\left( {5 \times 5 \times 5 \times 5} \right)^{\frac{3}{4}}} \cr
& = {\left( {{5^4}} \right)^{\frac{3}{4}}} \cr
& = {5^3} \cr
& = 125 \cr} $$
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$$\eqalign{
& {\text{Given,}} \cr
& = \root 4 \of {{{\left( {625} \right)}^3}} \cr
& = {\left( {625} \right)^{\frac{3}{4}}} \cr
& = {\left( {5 \times 5 \times 5 \times 5} \right)^{\frac{3}{4}}} \cr
& = {\left( {{5^4}} \right)^{\frac{3}{4}}} \cr
& = {5^3} \cr
& = 125 \cr} $$
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