Question

SIMPLIFY-
3 raise to -5 x 10 raise to -5 x 125 / 6 raise to -5 x 5 raise to -7

Answer 1

$$\begin{gathered} \frac{3^{-5}\times {10}^{-5}\times 125}{6^{-5}\times 5^{-7}} \\ =\frac{3^{-5}\times {\left(2\times 5\right)}^{-5}\times 5^3}{{\left(2\times 3\right)}^{-5}\times 5^{-7}},\mathrm{law}\mathrm{of}\mathrm{exponent}{\left(a\times b\right)}^m=a^m\times a^n \\ =\frac{3^{-5}\times 2^{-5}\times 5^{-5}\times 5^3}{2^{-5}\times 3^{-5}\times 5^{-7}} \\ =\frac{5^{-5+3}}{5^{-7}}=\frac{5^{-2}}{5^{-7}},\mathrm{law}\mathrm{of}\mathrm{exponent}{a}^m\times a^n=a^{m+n} \\ =5^{-2-\left(-7\right)}=5^{-2+7},\mathrm{law}\mathrm{of}\mathrm{exponent}\frac{a^m}{a^n}=a^{m-n} \\ =5^5=3125 \end{gathered}$$