Solve for x x^(2/3)-60=40

$x^{\frac{2}{3}} - 60 = 40$

Move all terms not containing $x$ to the right side of the equation.

Add $60$ to both sides of the equation.

$x^{\frac{2}{3}} - 40 = 60$

Add $40$ to both sides of the equation.

$x^{\frac{2}{3}} = 60 + 40$

Add $60$ and $40$ .

$x^{\frac{2}{3}} = 100$

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 100^{\frac{3}{2}}$

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Multiply the exponents in ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 100^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 100^{\frac{3}{2}}$

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 100^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 100^{\frac{3}{2}}$

Rewrite the expression.

$x^{1} = \pm 100^{\frac{3}{2}}$

Simplify.

$x = \pm 100^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 100^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $100$ as $10^{2}$ .

$x = \pm {(10^{2})}^{\frac{3}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm 10^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \pm 10^{2 (\frac{3}{2})}$

Rewrite the expression.

$x = \pm 10^{3}$

Raise $10$ to the power of $3$ .

$x = \pm 1000$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 1000$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1000$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1000, - 1000$

Solve for x x^(2/3)-60=40

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