Simplify 3 fourth root of z*3z^(3/4)

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

Step 1

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

Multiply $3$ by $3$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $3$ and $1$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$9 z^{1}$

Step 2

Simplify.

$9 z$