Question

3 to the power minus 5 into 10 to the power minus 5 into 125 / 5 to the power minus 7 into 6 to the power minus 7

Answer 1

Answer:

(-7)*(-279936)= 1959552

Answer 2

Answer:

$\frac{3^{-5}*10^{-5}*125}{5^{-7}*6^{-7}}$ = 112500

Step-by-step explanation:

Given expression : $\frac{3^{-5}*10^{-5}*125}{5^{-7}*6^{-7}}$

We know that 5³ = 125

Therefore,  $\frac{3^{-5}*10^{-5}*125}{5^{-7}*6^{-7}}$ =  $\frac{3^{-5}*10^{-5}*5^3}{5^{-7}*6^{-7}}$

We also know that (a*b)ⁿ = aⁿ * bⁿ

=>   $\frac{3^{-5}*10^{-5}*5^3}{5^{-7}*6^{-7}}$ =   $\frac{3^{-5}*(2*5)^{-5}*5^3}{5^{-7}*(2*3)^{-7}}$ =  $\frac{3^{-5}*2^{-5}*5^{-5}*5^3}{5^{-7}*2^{-7}*3^{-7}}$

As  $a^n *a^m = a^{n+m}$

=>  $\frac{3^{-5}*2^{-5}*5^{-5}*5^3}{5^{-7}*2^{-7}*3^{-7}}$ =  $\frac{3^{-5}*2^{-5}*5^{-5+3}}{5^{-7}*2^{-7}*3^{-7}}$ =  $\frac{3^{-5}*2^{-5}*5^{-2}}{5^{-7}*2^{-7}*3^{-7}}$

As $\frac{a^n}{a^m} = a^{n-m}$

=>  $\frac{3^{-5}*2^{-5}*5^{-2}}{5^{-7}*2^{-7}*3^{-7}}$ =  3⁻⁵⁻⁽⁻⁷⁾ *2⁻⁵⁻⁽⁻⁷⁾ * 5⁻²⁻⁽⁻⁷⁾

                       = 3² * 2² * 5⁵

                       = 9 * 4 * 3125

                       = 112500

Therefore,  $\frac{3^{-5}*10^{-5}*125}{5^{-7}*6^{-7}}$ = 112500