Simplify 4/(5a^3b^2)+(9c)/(10ab)

$\frac{4}{5 a^{3} b^{2}} + \frac{9 c}{10 a b}$

To write $\frac{4}{5 a^{3} b^{2}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4}{5 a^{3} b^{2}} \cdot \frac{2}{2} + \frac{9 c}{10 a b}$

To write $\frac{9 c}{10 a b}$ as a fraction with a common denominator, multiply by $\frac{a^{2} b}{a^{2} b}$ .

$\frac{4}{5 a^{3} b^{2}} \cdot \frac{2}{2} + \frac{9 c}{10 a b} \cdot \frac{a^{2} b}{a^{2} b}$

Write each expression with a common denominator of $10 a^{3} b^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{5 a^{3} b^{2}}$ by $\frac{2}{2}$ .

$\frac{4 \cdot 2}{5 a^{3} b^{2} \cdot 2} + \frac{9 c}{10 a b} \cdot \frac{a^{2} b}{a^{2} b}$

Multiply $2$ by $5$ .

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c}{10 a b} \cdot \frac{a^{2} b}{a^{2} b}$

Multiply $\frac{9 c}{10 a b}$ by $\frac{a^{2} b}{a^{2} b}$ .

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a b (a^{2} b)}$

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

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 (a^{2} a^{1}) b \cdot b}$

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

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{2 + 1} b \cdot b}$

Add $2$ and $1$ .

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{3} b \cdot b}$

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

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{3} (b^{1} b)}$

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

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{3} (b^{1} b^{1})}$

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

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{3} b^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \cdot 2}{10 a^{3} b^{2}} + \frac{9 c (a^{2} b)}{10 a^{3} b^{2}}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 9 c (a^{2} b)}{10 a^{3} b^{2}}$

Multiply $4$ by $2$ .

$\frac{8 + 9 c a^{2} b}{10 a^{3} b^{2}}$