Question

How do you simplify `\frac { u ^ { 32} } { u ^ { 9} \cdot u ^ { - 23} \cdot u ^ { 26} }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule for exponents to simplify the denominator:

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

`u^32/(u^color(red)(9) * u^color(blue)(-23) * u^color(green)(26)) = u^32/(u^(color(red)(9) + color(blue)(-23) + color(green)(26))) = u^32/(u^(color(red)(9) - color(blue)(23) + color(green)(26))) = u^32/u^12`

Now, use this rule for exponents to complete the simplification:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`u^color(red)(32)/u^color(blue)(12) = u^(color(red)(32)-color(blue)(12)) = u^20`