Question

How do you simplify `(4w ^ { - 5} x ^ { 4} ) ^ { - 3}`?

Answer 1

See the entire solution process below:

Explanation:

First, use these two rules of exponents to eliminate the outer exponent:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(4w^-5x^4)^-3 = (4^color(red)(1)w^color(red)(-5)x^color(red)(4))^color(blue)(-3) = 4^(color(red)(1) xx color(blue)(-3))w^(color(red)(-5) xx color(blue)(-3))x^(color(red)(4) xx color(blue)(-3)) =`

`4^-3w^15x^-12`

Now, use this rule of exponents to eliminate the negative exponents:

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

`x^color(red)(-3)w^15x^color(red)(-12) = w^15/(4^color(red)(--3)x^color(red)(- -12)) = w^15/(4^3x^12) = w^15/(64x^12)`