Question

Select the equivilent expression(4 ^ 3 / 5 to the negative power of two) ^ 5

Answer 1

A rule that we need to know in order to solve this is:

`(a^b)^c=a^(bc)`

The extended rule would be:

`((a^b)/(c^d))^x=(a^(bx))/(c^(dx))`

Also, remember another rule:

`(1)/(a^(-x))=a^x`

Keeping all these rules in mind, we can simplify:

`((4^3)/(5^(-2)))^5=(4^(15))/(5^(-10))=4^(15)\cdot5^(10)`

THis is the final form.