Question

Find the value of $\frac{{\left(625\right)}^{6.25}\times {\left(25\right)}^{2.60}}{{\left(625\right)}^{7.25}\times {\left(5\right)}^{1.20}}$

Answer 1

$\frac{{\left(625\right)}^{6.25}\times {\left(25\right)}^{2.60}}{{\left(625\right)}^{7.25}\times {\left(5\right)}^{1.20}}$

$=\frac{(625{)}^{6.25-7.25}\times (5^2{)}^{2.60}}{(5{)}^{1.20}}$ ....... [Using quotient rule of exponents]

$=\frac{(625{)}^{-1.00}\times (5{)}^{5.20}}{(5{)}^{1.20}}$

$=\frac{(5{)}^{5.20-1.20}}{\left(625\right)}$ ....... [Using quotient law of exponents]

$=\frac{(5{)}^4}{5^4}$

$=1$

Hence, $\frac{{\left(625\right)}^{6.25}\times {\left(25\right)}^{2.60}}{{\left(625\right)}^{7.25}\times {\left(5\right)}^{1.20}}=1$