Algebra Examples

$\frac{3 \sqrt{2}}{2} \cdot \sqrt{2}$

Step 1

Multiply $\frac{3 \sqrt{2}}{2} \sqrt{2}$ .

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Step 1.1

Combine $\frac{3 \sqrt{2}}{2}$ and $\sqrt{2}$ .

$\frac{3 \sqrt{2} \sqrt{2}}{2}$

Step 1.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 ({\sqrt{2}}^{1} \sqrt{2})}{2}$

Step 1.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2}$

Step 1.4

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

$\frac{3 {\sqrt{2}}^{1 + 1}}{2}$

Step 1.5

Add $1$ and $1$ .

$\frac{3 {\sqrt{2}}^{2}}{2}$

Step 2

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

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Step 2.1

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

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

Step 2.2

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

$\frac{3 \cdot 2^{\frac{1}{2} \cdot 2}}{2}$

Step 2.3

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

$\frac{3 \cdot 2^{\frac{2}{2}}}{2}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\frac{3 \cdot 2^{\frac{2}{2}}}{2}$

Step 2.4.2

Rewrite the expression.

$\frac{3 \cdot 2^{1}}{2}$

Step 2.5

Evaluate the exponent.

$\frac{3 \cdot 2}{2}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $3$ by $2$ .

$\frac{6}{2}$

Step 3.2

Divide $6$ by $2$ .

$3$