# How do you multiply \frac { 6a ^ { 5} c } { 5a c ^ { 4} } \times \frac { 4a ^ { 3} } { 9a c ^ { 4} }?

Jul 20, 2017

Multiply all the top numbers and the same for the bottom numbers, just like a regular fraction multiplication. Group like unknowns and add their exponents. You will end up with a single fraction.

#### Explanation:

We have: $\frac{6 {a}^{5} c}{5 a {c}^{4}} \times \frac{4 {a}^{3}}{9 a {c}^{4}}$

Numbers:
$6 \times 4 = 24$
$5 \times 9 = 45$

Top:
${a}^{5} \times {a}^{3} = {a}^{8}$
$c \times 1 = c$

Bottom:
$a \times a = {a}^{2}$
${c}^{4} \times {c}^{4} = {c}^{8}$

Re-assembling:
(24a^8c)/(45a^2c^8

Cancelling the divided unknowns exponents by subtraction:
(24cancel(a^8)a^6cancelc)/(45cancel(a^2)cancel(c^8)c^7

Then:
$\frac{6 {a}^{5} c}{5 a {c}^{4}} \times \frac{4 {a}^{3}}{9 a {c}^{4}} = \frac{24 {a}^{6}}{45 {c}^{7}} = \frac{8 {a}^{6}}{15 {c}^{7}}$