Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Add $1$ and $3$ .

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

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Cancel the common factor.

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

Step 1.6.2

Rewrite the expression.

$3^{1}$

Step 2

Evaluate the exponent.

$3$