Algebra Examples

$3^{- \frac{1}{4}} \cdot 27^{- \frac{1}{4}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{\frac{1}{4}}} \cdot 27^{- \frac{1}{4}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{\frac{1}{4}}} \cdot \frac{1}{27^{\frac{1}{4}}}$

Step 3

Combine fractions.

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Step 3.1

Combine.

$\frac{1 \cdot 1}{3^{\frac{1}{4}} \cdot 27^{\frac{1}{4}}}$

Step 3.2

Multiply $1$ by $1$ .

$\frac{1}{3^{\frac{1}{4}} \cdot 27^{\frac{1}{4}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $27$ as $3^{3}$ .

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

Step 4.2

Multiply the exponents in ${(3^{3})}^{\frac{1}{4}}$ .

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Step 4.2.1

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

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

Step 4.2.2

Combine $3$ and $\frac{1}{4}$ .

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Add $1$ and $3$ .

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

Step 4.6

Cancel the common factor of $4$ .

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Step 4.6.1

Cancel the common factor.

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

Step 4.6.2

Rewrite the expression.

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

Step 5

Evaluate the exponent.

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$