How do you simplify #(q^(1/5))^5times(q^(2/3))^3#?

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Answer 1 · 2017-01-03T22:18:27

Use various rules for exponents to simplify this expression. See explanation below.

The first rule for exponents will will utilize is:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

This simplifies our expression to:

#q^(color(red)(1/5) xx color(blue)(5)) xx q^(color(red)(2/3) xx color(blue)(3)) = #

#q^(color(red)(1)) xx q^(color(red)(2)#

The next rule of exponents we can use is:

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

Using this rule allows us to simplify our expression to:

#q^(color(red)(1)+color(red)(2)) = #

#q^3#