Question

Simplify the following question given above

Answer 1

Answer:

a) 5⁵ = 3125

Step-by-step explanation:

Explanation:-

Given  

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

on simplification , we get

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

By using algebraic formula

(ab)ⁿ = aⁿ b ⁿ      

 

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

after cancellation , we get

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

      =   $(5)^{-5} X(5)^{3} X (5)^{7}$

      = 5⁻⁵⁺³⁺⁷

     = 5⁵

    = 3125

final answer:-

$\frac{3^{-5} X 10^{-5} X 125 }{5^{-7} X 6 ^{-5} } = 3125$