Algebra Examples

$9^{\frac{1}{4}} \cdot 9^{\frac{1}{4}}$

Step 1

Multiply $9^{\frac{1}{4}}$ by $9^{\frac{1}{4}}$ by adding the exponents.

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Step 1.1

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

$9^{\frac{1}{4} + \frac{1}{4}}$

Step 1.2

Combine the numerators over the common denominator.

$9^{\frac{1 + 1}{4}}$

Step 1.3

Add $1$ and $1$ .

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

Step 1.4

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

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Step 1.4.1

Factor $2$ out of $2$ .

$9^{\frac{2 (1)}{4}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $2$ out of $4$ .

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 1.4.2.2

Cancel the common factor.

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 1.4.2.3

Rewrite the expression.

$9^{\frac{1}{2}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

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

Step 2.2

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$3^{1}$

Step 4

Evaluate the exponent.

$3$