# Solve for w 1 = cube root of 4w^2 1=4w23
Rewrite the equation as 4w23=1.
4w23=1
To remove the radical on the left side of the equation, cube both sides of the equation.
4w233=13
Simplify each side of the equation.
Multiply the exponents in ((4w2)13)3.
Apply the power rule and multiply exponents, (am)n=amn.
(4w2)13⋅3=13
Cancel the common factor of 3.
Cancel the common factor.
(4w2)13⋅3=13
Rewrite the expression.
(4w2)1=13
(4w2)1=13
(4w2)1=13
Simplify.
4w2=13
One to any power is one.
4w2=1
4w2=1
Solve for w.
Divide each term by 4 and simplify.
Divide each term in 4w2=1 by 4.
4w24=14
Cancel the common factor of 4.
Cancel the common factor.
4w24=14
Divide w2 by 1.
w2=14
w2=14
w2=14
Take the square root of both sides of the equation to eliminate the exponent on the left side.
w=±14
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 14 as 14.
w=±14
Any root of 1 is 1.
w=±14
Simplify the denominator.
Rewrite 4 as 22.
w=±122
Pull terms out from under the radical, assuming positive real numbers.
w=±12
w=±12
w=±12
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
w=12
Next, use the negative value of the ± to find the second solution.
w=-12
The complete solution is the result of both the positive and negative portions of the solution.
w=12,-12
w=12,-12
w=12,-12
w=12,-12
The result can be shown in multiple forms.
Exact Form:
w=12,-12
Decimal Form:
w=0.5,-0.5
Solve for w 1 = cube root of 4w^2

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