Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factor of $2$ .

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Step 1.3.2.1

Cancel the common factor.

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

Step 1.3.2.2

Rewrite the expression.

$9 y^{3} = 72 x$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

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

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Step 2.3.1.1

Factor $9$ out of $72 x$ .

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

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $9$ out of $9$ .

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

Step 2.3.1.2.2

Cancel the common factor.

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

Step 2.3.1.2.3

Rewrite the expression.

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

Step 2.3.1.2.4

Divide $8 x$ by $1$ .

$y^{3} = 8 x$

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Pull terms out from under the radical.

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