Question

30 POINTS!!!!!!!!!!!!!!!!!!!!!! 4 x times the fraction 1 over x to the power of negative 5 times x to the power of negative 3

Answer 1

`4 {x}^(3)`

Explanation:

We want to simplify

`4x * ( (1)/(x))^( - 5) * {x}^( - 3)`

Recall the reciprocal property:

`(1)/(a) = {a}^( - 1)`

We apply this property to get:

`4x * ( {x}^( - 1) )^( - 5) * {x}^( - 3)`

Also apply this property of exponents to get:

`{(a}^(m))^(n) = {a}^(mn)`

`4x * ( x )^( 5) * {x}^( - 3)`

We simplify using the product property of exponents to get:

`4 {x}^(1 + 5 - 3) = 4 {x}^(3)`