Write the Fraction in Simplest Form (6z)/(2(z^2)^5)

$\frac{6 z}{2 {(z^{2})}^{5}}$

Step 1

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 z$ .

$\frac{2 (3 z)}{2 {(z^{2})}^{5}}$

Cancel the common factors.

Factor $2$ out of $2 {(z^{2})}^{5}$ .

$\frac{2 (3 z)}{2 ({(z^{2})}^{5})}$

Cancel the common factor.

$\frac{2 (3 z)}{2 {(z^{2})}^{5}}$

Rewrite the expression.

$\frac{3 z}{{(z^{2})}^{5}}$

Step 2

Multiply the exponents in ${(z^{2})}^{5}$ .

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

$\frac{3 z}{z^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{3 z}{z^{10}}$

Step 3

Cancel the common factor of $z$ and $z^{10}$ .

Factor $z$ out of $3 z$ .

$\frac{z \cdot 3}{z^{10}}$

Cancel the common factors.

Factor $z$ out of $z^{10}$ .

$\frac{z \cdot 3}{z \cdot z^{9}}$

Cancel the common factor.

$\frac{z \cdot 3}{z \cdot z^{9}}$

Rewrite the expression.

$\frac{3}{z^{9}}$