Question

How do you simplify `u^2*u*u^-6`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the middle `u` term:

`a = a^color(blue)(1)`

`u^2 * u * u^-6 => u^2 * u^color(blue)(1) * u^-6`

Next, use this rule of exponents to multiply the three `u` terms:

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

`u^color(red)(2) * u^color(blue)(1) * u^color(green)(-6) => u^(color(red)(2)+color(blue)(1)+color(green)(-6)) => u^-3`

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

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

`u^color(red)(-6) => 1/u^color(red)(- -6) => 1/u^6`