Algebra Examples

$3 \sqrt[4]{z} \cdot 3 z^{\frac{3}{4}}$

Step 1

Multiply $3$ by $3$ .

$9 \sqrt[4]{z} z^{\frac{3}{4}}$

Step 2

Multiply $9 \sqrt[4]{z} z^{\frac{3}{4}}$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{z}$ as $z^{\frac{1}{4}}$ .

$9 (z^{\frac{3}{4}} z^{\frac{1}{4}})$

Step 2.2

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

$9 z^{\frac{3}{4} + \frac{1}{4}}$

Step 2.3

Combine the numerators over the common denominator.

$9 z^{\frac{3 + 1}{4}}$

Step 2.4

Add $3$ and $1$ .

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

Step 2.5

Cancel the common factor of $4$ .

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Step 2.5.1

Cancel the common factor.

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

Step 2.5.2

Rewrite the expression.

$9 z^{1}$

Step 3

Simplify.

$9 z$