How do you simplify #(5a^(1/7)b^(5/7))^3#?

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Answer 1 · 2016-10-15T19:55:16

#125a^(3/7)b^(15/7)#

#(5a^(1/7)b^(5/7))^3#

Use the exponent rule #(x^a)^b=x^(ab)#

First, recall that when there is no exponent written, there is an exponent of #color(red)1#.

#(5^color(red)1a^(1/7)b^(5/7))^color(blue)3#

Each part inside the fraction must be "raised to the power" 3. The exponents are then multiplied.

#5^(color(red)1*color(blue)3)a^(1/7*color(blue)3)b^(5/7*color(blue)3#

#1/7*3=1/7*3/1=3/7# and #5/7*3=5/7*3/1=15/7#

#5^3a^(3/7)b^(15/7)#

#5^3=5*5*5=125#

#125a^(3/7)b^(15/7)#