Algebra Examples

${(\frac{1}{\sqrt{3}})}^{7}$

Step 1

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

${(\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})}^{7}$

Step 2

Combine fractions.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

${(\frac{\sqrt{3}}{\sqrt{3} \sqrt{3}})}^{7}$

Step 2.1.2

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

${(\frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}})}^{7}$

Step 2.1.3

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

${(\frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}})}^{7}$

Step 2.1.4

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

${(\frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}})}^{7}$

Step 2.1.5

Add $1$ and $1$ .

${(\frac{\sqrt{3}}{{\sqrt{3}}^{2}})}^{7}$

Step 2.1.6

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

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Step 2.1.6.1

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

${(\frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}})}^{7}$

Step 2.1.6.2

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

${(\frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}})}^{7}$

Step 2.1.6.3

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

${(\frac{\sqrt{3}}{3^{\frac{2}{2}}})}^{7}$

Step 2.1.6.4

Cancel the common factor of $2$ .

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Step 2.1.6.4.1

Cancel the common factor.

${(\frac{\sqrt{3}}{3^{\frac{2}{2}}})}^{7}$

Step 2.1.6.4.2

Rewrite the expression.

${(\frac{\sqrt{3}}{3^{1}})}^{7}$

Step 2.1.6.5

Evaluate the exponent.

${(\frac{\sqrt{3}}{3})}^{7}$

Step 2.2

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

$\frac{{\sqrt{3}}^{7}}{3^{7}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt{3}}^{7}$ as $\sqrt{3^{7}}$ .

$\frac{\sqrt{3^{7}}}{3^{7}}$

Step 3.2

Raise $3$ to the power of $7$ .

$\frac{\sqrt{2187}}{3^{7}}$

Step 3.3

Rewrite $2187$ as $27^{2} \cdot 3$ .

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Step 3.3.1

Factor $729$ out of $2187$ .

$\frac{\sqrt{729 (3)}}{3^{7}}$

Step 3.3.2

Rewrite $729$ as $27^{2}$ .

$\frac{\sqrt{27^{2} \cdot 3}}{3^{7}}$

Step 3.4

Pull terms out from under the radical.

$\frac{27 \sqrt{3}}{3^{7}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Raise $3$ to the power of $7$ .

$\frac{27 \sqrt{3}}{2187}$

Step 4.2

Cancel the common factor of $27$ and $2187$ .

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Step 4.2.1

Factor $27$ out of $27 \sqrt{3}$ .

$\frac{27 (\sqrt{3})}{2187}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $27$ out of $2187$ .

$\frac{27 \sqrt{3}}{27 \cdot 81}$

Step 4.2.2.2

Cancel the common factor.

$\frac{27 \sqrt{3}}{27 \cdot 81}$

Step 4.2.2.3

Rewrite the expression.

$\frac{\sqrt{3}}{81}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{81}$

Decimal Form:

$0.02138334 \dots$