Question

Simplify the following question given above

Answer 1

a) 5⁵ = 3125

Explanation:

Explanation:-

Given

`(3^(-5) X 10^(-5) X 125 )/(5^(-7) X 6 ^(-5) )`

on simplification , we get

=
`(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

=
`( (5)^(-5) X(5)^(3) )/(5^(-7) )`

=
`(5)^(-5) X(5)^(3) X (5)^(7)`

= 5⁻⁵⁺³⁺⁷

= 5⁵

= 3125

final answer:-

`(3^(-5) X 10^(-5) X 125 )/(5^(-7) X 6 ^(-5) ) = 3125`