Solve for y -3(y-2)^(2/3)+29=-19

$- 3 {(y - 2)}^{\frac{2}{3}} + 29 = - 19$

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

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Subtract $29$ from both sides of the equation.

$- 3 {(y - 2)}^{\frac{2}{3}} = - 19 - 29$

Subtract $29$ from $- 19$ .

$- 3 {(y - 2)}^{\frac{2}{3}} = - 48$

Divide each term by $- 3$ and simplify.

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Divide each term in $- 3 {(y - 2)}^{\frac{2}{3}} = - 48$ by $- 3$ .

$\frac{- 3 {(y - 2)}^{\frac{2}{3}}}{- 3} = \frac{- 48}{- 3}$

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

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Cancel the common factor.

$\frac{- 3 {(y - 2)}^{\frac{2}{3}}}{- 3} = \frac{- 48}{- 3}$

Divide ${(y - 2)}^{\frac{2}{3}}$ by $1$ .

${(y - 2)}^{\frac{2}{3}} = \frac{- 48}{- 3}$

Divide $- 48$ by $- 3$ .

${(y - 2)}^{\frac{2}{3}} = 16$

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

${({(y - 2)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm {(16)}^{\frac{3}{2}}$

Solve the equation for $y$ .

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Simplify the right side of the equation.

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Simplify the expression.

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Rewrite $16$ as $4^{2}$ .

$y - 2 = \pm {(4^{2})}^{\frac{3}{2}}$

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

$y - 2 = \pm 4^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$y - 2 = \pm 4^{2 (\frac{3}{2})}$

Rewrite the expression.

$y - 2 = \pm 4^{3}$

Raise $4$ to the power of $3$ .

$y - 2 = \pm 64$

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

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

$y - 2 = 64$

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

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Add $2$ to both sides of the equation.

$y = 64 + 2$

Add $64$ and $2$ .

$y = 66$

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

$y - 2 = - 64$

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

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Add $2$ to both sides of the equation.

$y = - 64 + 2$

Add $- 64$ and $2$ .

$y = - 62$

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

$y = 66, - 62$

Solve for y -3(y-2)^(2/3)+29=-19

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