How do you solve #(4x + 5) ^ { \frac{ 1}{ 3} } = 1#?

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Answer 1 · 2017-01-03T13:26:25

Raise each side of the equation to the 3rd power and then solve. See full solution below:

First, we raise each side of the equation to the third power:

#((4x + 5)^(1/3))^color(red)(3) = 1^color(red)(3)#

Using these two rules we simplify the terms on each side of the equation:

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

#1^color(red)(x) = 1#

Giving

#(4x + 5)^(1/3 xx 3) = 1#

#(4x + 5)^1 = 1#

The next rule of exponents we can use is:

#x^color(red)(1) = x#

Resulting in:

#4x + 5 = 1#

Now we can solve this as an ordinary linear equation:

#4x + 5 - color(red)(5) = 1 - color(red)(5)#

#4x + 0 = -4#

#4x = -4#

#(4x)/color(red)(4) = -4/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -1#

#x = -1#