Question

$\frac{5^{10+n}\times {25}^{3n-4}}{5^{7n}}$ = _____

• A. 10
• B. 25
• C. 20
• D. 15

Answer 1

The correct option is B 25

$\frac{5^{10+n}\times {25}^{3n-4}}{5^{7n}}$

$=\frac{5^{10+n}\times (5^2{)}^{3n-4}}{5^{7n}}$ [Since 25 = 5 x 5]

$=\frac{5^{10+n}\times 5^{6n-8}}{5^{7n}}$ $[\because (a^m{)}^n=\left(a{)}^{m\times n}\right]$

$=\frac{5^{10+n+6n-8}}{5^{7n}}$ $[\because a^m\times a^n=a^{(m+n)}]$

$=\frac{5^{7n+2}}{5^{7n}}$

$=5^{7n+2-7n}$ $[\because \frac{a^m}{a^n}=a^{(m-n)}]$

$=5^2$

$=25$