Solve for y (3y^(3/2))^2=72x

${(3 y^{\frac{3}{2}})}^{2} = 72 x$

Step 1

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

Apply the product rule to $3 y^{\frac{3}{2}}$ .

$3^{2} {(y^{\frac{3}{2}})}^{2} = 72 x$

Raise $3$ to the power of $2$ .

$9 {(y^{\frac{3}{2}})}^{2} = 72 x$

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

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

$9 y^{\frac{3}{2} \cdot 2} = 72 x$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 y^{\frac{3}{2} \cdot 2} = 72 x$

Rewrite the expression.

$9 y^{3} = 72 x$

Step 2

Divide each term in $9 y^{3} = 72 x$ by $9$ and simplify.

Divide each term in $9 y^{3} = 72 x$ by $9$ .

$\frac{9 y^{3}}{9} = \frac{72 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y^{3}}{9} = \frac{72 x}{9}$

Divide $y^{3}$ by $1$ .

$y^{3} = \frac{72 x}{9}$

Simplify the right side.

Cancel the common factor of $72$ and $9$ .

Factor $9$ out of $72 x$ .

$y^{3} = \frac{9 (8 x)}{9}$

Cancel the common factors.

Factor $9$ out of $9$ .

$y^{3} = \frac{9 (8 x)}{9 (1)}$

Cancel the common factor.

$y^{3} = \frac{9 (8 x)}{9 \cdot 1}$

Rewrite the expression.

$y^{3} = \frac{8 x}{1}$

Divide $8 x$ by $1$ .

$y^{3} = 8 x$

Step 3

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[3]{8 x}$

Step 4

Simplify $\sqrt[3]{8 x}$ .

Rewrite $8$ as $2^{3}$ .

$y = \sqrt[3]{2^{3} x}$

Pull terms out from under the radical.

$y = 2 \sqrt[3]{x}$

Solve for y (3y^(3/2))^2=72x

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