Question

How do you simplify `(\frac { 3} { 5} ) ^ { 3} \cdot ( \frac { 3} { 4} ) ^ { - 2} \cdot ( - \frac { 5} { 4} ) ^ { 4}`?

Answer 1

`15/16`

Explanation:

`=3^3*5^-3*3^2*4^-2*(-5)^4*(-4)^-4`
`3*5*4^-6=15/16`

Aliter :
`=(3^3*3^-2*(-5)^4)/(5^3*4^-2*(-4)^4)`
=`(3^(3-2)*5^(-3+4))/4^(-2+4)=(3*5)/4^2=15/16`