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

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

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