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

1 Answer
Mar 15, 2017

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#