Question

Exponent of the final value of $\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$ is :

• A. $5^4$
• B. $5^5$
• C. $2^5$
• D. $5^6$

Answer 1

The correct option is B

$5^5$

$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

= $\frac{3^{-5}\times (2\times 5{)}^{-5}\times 125}{5^{-7}\times (2\times 3{)}^{-5}}$

= $\frac{3^{-5}\times (2^{-5}\times 5^{-5})\times 5^3}{5^{-7}\times (2^{-5}\times 3^{-5})}$ ($\because (ab{)}^m=a^b\times b^m$)

= $\frac{3^{-5}\times 2^{-5}\times 5^{-2}}{5^{-7}\times 2^{-5}\times 3^{-5}}$ ($\because$ $a^m$ $\times$ $a^n$ = $a^{m+n}$)

= $5^5$