Basic Math Examples

$3^{3} \sqrt{9 a} \cdot (2^{3} \sqrt{3 a^{3}})$

Step 1

Simplify the expression.

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Step 1.1

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

$27 \sqrt{9 a} \cdot (2^{3} \sqrt{3 a^{3}})$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$27 \sqrt{3^{2} a} \cdot (2^{3} \sqrt{3 a^{3}})$

$27 \sqrt{3^{2} a} \cdot (2^{3} \sqrt{3 a^{3}})$

Step 2

Pull terms out from under the radical.

$27 (3 \sqrt{a}) \cdot (2^{3} \sqrt{3 a^{3}})$

Step 3

Simplify the expression.

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Step 3.1

Multiply $3$ by $27$ .

$81 \sqrt{a} \cdot (2^{3} \sqrt{3 a^{3}})$

Step 3.2

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

$81 \sqrt{a} \cdot (8 \sqrt{3 a^{3}})$

$81 \sqrt{a} \cdot (8 \sqrt{3 a^{3}})$

Step 4

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

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Step 4.1

Factor out $a^{2}$ .

$81 \sqrt{a} \cdot (8 \sqrt{3 (a^{2} a)})$

Step 4.2

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

$81 \sqrt{a} \cdot (8 \sqrt{a^{2} \cdot 3 a})$

Step 4.3

Add parentheses.

$81 \sqrt{a} \cdot (8 \sqrt{a^{2} \cdot (3 a)})$

$81 \sqrt{a} \cdot (8 \sqrt{a^{2} \cdot (3 a)})$

Step 5

Pull terms out from under the radical.

$81 \sqrt{a} \cdot (8 (a \sqrt{3 a}))$

Step 6

Multiply $81 \sqrt{a} (8 a \sqrt{3 a})$ .

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Step 6.1

Multiply $8$ by $81$ .

$648 \sqrt{a} (a \sqrt{3 a})$

Step 6.2

Combine using the product rule for radicals.

$648 (a \sqrt{a (3 a)})$

Step 6.3

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

$648 (a \sqrt{3 (a^{1} a)})$

Step 6.4

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

$648 (a \sqrt{3 (a^{1} a^{1})})$

Step 6.5

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

$648 (a \sqrt{3 a^{1 + 1}})$

Step 6.6

Add $1$ and $1$ .

$648 (a \sqrt{3 a^{2}})$

$648 (a \sqrt{3 a^{2}})$

Step 7

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

$648 (a \sqrt{a^{2} \cdot 3})$

Step 8

Pull terms out from under the radical.

$648 (a (a \sqrt{3}))$

Step 9

Multiply $a$ by $a$ by adding the exponents.

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Step 9.1

Move $a$ .

$648 (a \cdot a \sqrt{3})$

Step 9.2

Multiply $a$ by $a$ .

$648 (a^{2} \sqrt{3})$

$648 a^{2} \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$