Question

Help me out please?
chapter : exponents and powers​

Answer 1

`(125)/(27)`

Explanation:

Because it is the "Correct Answer"

Answer 2

`(125)/(27)`

Explanation:

`(2^(-4) * 15^(-3) * 625)/(5^2 * 10^(-4))`

Lets expand all the composite numbers into prime numbers.

`=> (2^(-4) * (3^(-3) * 5^(-3)) * 5^4)/(5^2 * (2^(-4) * 5^(-4)))`

Lets cancel
`2^(-4)` from numerator and denominator.

`=> (3^(-3) * 5^(-3) * 5^4)/(5^2 * 5^(-4))`

Using laws of exponents , lets solve this.

`=> (3^(-3) * 5^((-3 + 4)))/(5^(( 2 - 4)))`

`=> (3^(-3) * 5^(1))/(5^(-2))`

`=> 3^(-3) * 5^([1 - (-2)])`

`=> 3^(-3) * 5^(3)`

`=> (5^3)/(3^3) = (125)/(27)`