Algebra Examples

${(4 \sqrt{3 a^{3}})}^{2}$

Step 1

Rewrite $3 a^{3}$ as $a^{2} \cdot (3 a)$ .

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Step 1.1

Factor out $a^{2}$ .

${(4 \sqrt{3 (a^{2} a)})}^{2}$

Step 1.2

Reorder $3$ and $a^{2}$ .

${(4 \sqrt{a^{2} \cdot 3 a})}^{2}$

Step 1.3

Add parentheses.

${(4 \sqrt{a^{2} \cdot (3 a)})}^{2}$

Step 2

Pull terms out from under the radical.

${(4 (a \sqrt{3 a}))}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $4 a \sqrt{3 a}$ .

${(4 a)}^{2} {\sqrt{3 a}}^{2}$

Step 3.2

Apply the product rule to $4 a$ .

$4^{2} a^{2} {\sqrt{3 a}}^{2}$

Step 4

Raise $4$ to the power of $2$ .

$16 a^{2} {\sqrt{3 a}}^{2}$

Step 5

Rewrite ${\sqrt{3 a}}^{2}$ as $3 a$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 a}$ as ${(3 a)}^{\frac{1}{2}}$ .

$16 a^{2} {({(3 a)}^{\frac{1}{2}})}^{2}$

Step 5.2

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

$16 a^{2} {(3 a)}^{\frac{1}{2} \cdot 2}$

Step 5.3

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

$16 a^{2} {(3 a)}^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$16 a^{2} {(3 a)}^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

$16 a^{2} {(3 a)}^{1}$

Step 5.5

Simplify.

$16 a^{2} (3 a)$

Step 6

Rewrite using the commutative property of multiplication.

$16 \cdot 3 a^{2} a$

Step 7

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 7.1

Move $a$ .

$16 \cdot 3 (a \cdot a^{2})$

Step 7.2

Multiply $a$ by $a^{2}$ .

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Step 7.2.1

Raise $a$ to the power of $1$ .

$16 \cdot 3 (a^{1} a^{2})$

Step 7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 \cdot 3 a^{1 + 2}$

Step 7.3

Add $1$ and $2$ .

$16 \cdot 3 a^{3}$

Step 8

Multiply $16$ by $3$ .

$48 a^{3}$