Basic Math Examples

${(3 \sqrt{6 y})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $3 \sqrt{6 y}$ .

$3^{2} {\sqrt{6 y}}^{2}$

Step 1.2

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

$9 {\sqrt{6 y}}^{2}$

Step 2

Rewrite ${\sqrt{6 y}}^{2}$ as $6 y$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 y}$ as ${(6 y)}^{\frac{1}{2}}$ .

$9 {({(6 y)}^{\frac{1}{2}})}^{2}$

Step 2.2

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

$9 {(6 y)}^{\frac{1}{2} \cdot 2}$

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

$9 {(6 y)}^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$9 {(6 y)}^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$9 {(6 y)}^{1}$

Step 2.5

Simplify.

$9 (6 y)$

Step 3

Multiply $6$ by $9$ .

$54 y$