Question

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

• A. $5^5$
• B. $5^4$
• C. $5^2$
• D. $1$

Answer 1

Answer: (A)

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

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

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

$=3^{-5+5}\times 2^{-5+5}\times 5^{-5+3+7}$

$=5^5$

$=3125$