Algebra Examples

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

Step 1

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite ${\sqrt{3}}^{4}$ as $3^{2}$ .

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Step 2.1.1

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

$\frac{{(3^{\frac{1}{2}})}^{4}}{2^{4}}$

Step 2.1.2

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

$\frac{3^{\frac{1}{2} \cdot 4}}{2^{4}}$

Step 2.1.3

Combine $\frac{1}{2}$ and $4$ .

$\frac{3^{\frac{4}{2}}}{2^{4}}$

Step 2.1.4

Cancel the common factor of $4$ and $2$ .

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Step 2.1.4.1

Factor $2$ out of $4$ .

$\frac{3^{\frac{2 \cdot 2}{2}}}{2^{4}}$

Step 2.1.4.2

Cancel the common factors.

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Step 2.1.4.2.1

Factor $2$ out of $2$ .

$\frac{3^{\frac{2 \cdot 2}{2 (1)}}}{2^{4}}$

Step 2.1.4.2.2

Cancel the common factor.

$\frac{3^{\frac{2 \cdot 2}{2 \cdot 1}}}{2^{4}}$

Step 2.1.4.2.3

Rewrite the expression.

$\frac{3^{\frac{2}{1}}}{2^{4}}$

Step 2.1.4.2.4

Divide $2$ by $1$ .

$\frac{3^{2}}{2^{4}}$

Step 2.2

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

$\frac{9}{2^{4}}$

Step 3

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

$\frac{9}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{16}$

Decimal Form:

$0.5625$