Question

Simplify (-2x^4y^-3)^4

Answer 1

`( - 2 {x}^(4) {y}^( - 3) )^(4) = \frac{16 {x}^(16)}{ {y}^(12) }`

Explanation:

We want to simplify:

`( - 2 {x}^(4) {y}^( - 3) )^(4)`

We need to apply the exponential property for products of powers.

Recall that:

`( {a}^(m) * {a}^(n) )^(p) = {a}^(mp) * {a}^(np)`

We apply this rule to get:

`( - 2 {x}^(4) {y}^( - 3) )^(4) = ( { - 2)}^(4) x * {x}^(16) * {y}^( - 12)`

This simplifies to:

`( - 2 {x}^(4) {y}^( - 3) )^(4) = 16 {x}^(16) * {y}^( - 12)`

We rewrite as positive index to get:

`( - 2 {x}^(4) {y}^( - 3) )^(4) = \frac{16 {x}^(16)}{ {y}^(12) }`