Simplify 7/(6z^3)+2/(3z)

$\frac{7}{6 z^{3}} + \frac{2}{3 z}$

To write $\frac{2}{3 z}$ as a fraction with a common denominator, multiply by $\frac{2 z^{2}}{2 z^{2}}$ .

$\frac{7}{6 z^{3}} + \frac{2}{3 z} \cdot \frac{2 z^{2}}{2 z^{2}}$

Write each expression with a common denominator of $6 z^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3 z}$ by $\frac{2 z^{2}}{2 z^{2}}$ .

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{3 z (2 z^{2})}$

Multiply $2$ by $3$ .

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{6 z \cdot z^{2}}$

Multiply $z$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{6 (z^{2} z)}$

Multiply $z^{2}$ by $z$ .

Raise $z$ to the power of $1$ .

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{6 (z^{2} z^{1})}$

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

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{6 z^{2 + 1}}$

Add $2$ and $1$ .

$\frac{7}{6 z^{3}} + \frac{2 (2 z^{2})}{6 z^{3}}$

Combine the numerators over the common denominator.

$\frac{7 + 2 (2 z^{2})}{6 z^{3}}$

Multiply $2$ by $2$ .

$\frac{7 + 4 z^{2}}{6 z^{3}}$