Simplify square root of z^9* square root of z^10

$\sqrt{z^{9}} \cdot \sqrt{z^{10}}$

Step 1

Rewrite $z^{9}$ as ${(z^{4})}^{2} z$ .

Factor out $z^{8}$ .

$\sqrt{z^{8} z} \cdot \sqrt{z^{10}}$

Rewrite $z^{8}$ as ${(z^{4})}^{2}$ .

$\sqrt{{(z^{4})}^{2} z} \cdot \sqrt{z^{10}}$

Step 2

Pull terms out from under the radical.

$z^{4} \sqrt{z} \cdot \sqrt{z^{10}}$

Step 3

Rewrite $z^{10}$ as ${(z^{5})}^{2}$ .

$z^{4} \sqrt{z} \cdot \sqrt{{(z^{5})}^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$z^{4} \sqrt{z} \cdot z^{5}$

Step 5

Multiply $z^{4}$ by $z^{5}$ by adding the exponents.

Move $z^{5}$ .

$z^{5} z^{4} \sqrt{z}$

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

$z^{5 + 4} \sqrt{z}$

Add $5$ and $4$ .

$z^{9} \sqrt{z}$