Question

What is the value of $\frac{{50}^2}{2^2\times 5^4}$?

• A. $\frac{25}{4}$
• B. $\frac{625}{100}$
• C. $\frac{2500}{625}$
• D. $1$

Answer 1

The correct option is D $1$

$\frac{{50}^2}{2^2\times 5^4}=\frac{{50}^2}{2^2\times 5^2\times 5^2}=\frac{{50}^2}{2^2\times 25\times 25}=\frac{{50}^2}{2^2\times {25}^2}=\frac{{50}^2}{(2\times 25{)}^2}(a^m\times b^m=(ab{)}^m)=\frac{{50}^2}{{50}^2}$
$=1$
OR,

$\frac{{50}^2}{2^2\times 5^4}=\frac{(2\times 25{)}^2}{2^2\times 5^4}$
$=\frac{(2\times 5^2{)}^2}{2^2\times 5^4}$
$=\frac{2^2\times (5^2{)}^2}{2^2\times 5^4}(\because (a\times b{)}^m=a^m\times b^m)$
$=\frac{2^2\times 5^4}{2^2\times 5^4}$
$=1$