Algebra Examples

$\frac{5 \sqrt{3}}{2} \cdot \sqrt{3}$

Step 1

Multiply $\frac{5 \sqrt{3}}{2} \sqrt{3}$ .

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Step 1.1

Combine $\frac{5 \sqrt{3}}{2}$ and $\sqrt{3}$ .

$\frac{5 \sqrt{3} \sqrt{3}}{2}$

Step 1.2

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{5 ({\sqrt{3}}^{1} \sqrt{3})}{2}$

Step 1.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{5 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}{2}$

Step 1.4

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

$\frac{5 {\sqrt{3}}^{1 + 1}}{2}$

Step 1.5

Add $1$ and $1$ .

$\frac{5 {\sqrt{3}}^{2}}{2}$

Step 2

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

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Step 2.1

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

$\frac{5 {(3^{\frac{1}{2}})}^{2}}{2}$

Step 2.2

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

$\frac{5 \cdot 3^{\frac{1}{2} \cdot 2}}{2}$

Step 2.3

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

$\frac{5 \cdot 3^{\frac{2}{2}}}{2}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\frac{5 \cdot 3^{\frac{2}{2}}}{2}$

Step 2.4.2

Rewrite the expression.

$\frac{5 \cdot 3^{1}}{2}$

Step 2.5

Evaluate the exponent.

$\frac{5 \cdot 3}{2}$

Step 3

Multiply $5$ by $3$ .

$\frac{15}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$