Question

$\frac{(625{)}^{6.25}\times (25{)}^{2.6}}{(625{)}^{6.75}\times (5{)}^{1.2}}=?$

• A. $5$
• B. $10$
• C. $15$
• D. $25$

Answer 1

The correct option is D $25$

Given,

$\frac{{625}^{6.25}\cdot {25}^{2.6}}{{625}^{6.75}\cdot 5^{1.2}}$

$=\frac{{625}^{\frac{25}{4}}\cdot {25}^{\frac{13}{5}}}{{625}^{\frac{27}{4}}\cdot 5^{\frac{6}{5}}}$

$=\frac{(5^4{)}^{\frac{25}{4}}\cdot (5^2{)}^{\frac{13}{5}}}{(5^4{)}^{\frac{27}{4}}\cdot 5^{\frac{6}{5}}}$

$=\frac{\left(5^{25}\right)\cdot (5{)}^{\frac{26}{5}}}{(5{)}^{27}\cdot 5^{\frac{6}{5}}}$

$=\frac{5^{25+\frac{26}{5}}}{5^{27+\frac{6}{5}}}$

$=5^{25+\frac{26}{5}-27-\frac{6}{5}}$

$=5^{-2+\frac{20}{5}}$

$=5^{-2+4}$

$=5^2=25$