Question

How do you simplify `(7s ^ { 4} t ^ { 3} u ^ { - 3} ) ^ { - 2}`?

Answer 1

See the entire solution process below:

Explanation:

Use these two rules of exponents to eliminate the out exponent:

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

`(7s^4t^3u^-3)^-2 = (7^color(red)(1)s^color(red)(4)t^color(red)(3)u^color(red)(-3))^color(blue)(-2) = 7^(color(red)(1) xx color(blue)(-2))s^(color(red)(4) xx color(blue)(-2))t^(color(red)(3) xx color(blue)(-2))u^(color(red)(-3) xx color(blue)(-2))`

`= 7^-2s^-8t^-6u^6`

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

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

`= 7^color(red)(-2)s^color(red)(-8)t^color(red)(-6)u^6 = u^6/(7^color(red)(- -2)s^color(red)(- -8)t^color(red)(- -6)) = u^6/(7^2s^8t^6) = u^6/(49s^8t^6)`