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 $5/7*3=5/7*3/1=15/7$

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

$5^3=5*5*5=125$

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

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