# How do you find the product of (3ad)/(4c^4)*(8c^2)/(6d)?

Dec 22, 2016

$\frac{a}{c} ^ 2$

#### Explanation:

$\frac{3 a d}{4 {c}^{4}} \cdot \frac{8 {c}^{2}}{6 d}$

cross-cancel:

$\frac{3 a d}{3 d} = a$

$\frac{6 d}{3 d} = 2$

$\frac{8 {c}^{2}}{4 {c}^{2}} = 2$

$\frac{4 {c}^{4}}{4 {c}^{2}} = {c}^{2}$

simplified equation:

$\frac{a}{c} ^ 2 \cdot \frac{2}{2}$

$= \frac{2 a}{2 {c}^{2}}$

$= \frac{a}{c} ^ 2$

Dec 22, 2016

$= \frac{a}{c} ^ 2$

#### Explanation:

Product means the answer to a mulitplication.

$\frac{3 a d}{4 {c}^{4}} \times \frac{8 {c}^{2}}{6 d} \text{ }$ cancel any like factors

$\frac{\cancel{3} a d}{\cancel{4} {c}^{4}} \times \frac{{\cancel{8}}^{2} {c}^{2}}{{\cancel{6}}^{2} d} \text{ } \leftarrow \frac{8 \div 4 = 2}{6 \div 3 = 2}$

Simplify into one numerator and one denominator

$= \frac{\cancel{2} a {c}^{2} \cancel{d}}{\cancel{2} {c}^{4} \cancel{d}}$

Simplify by subtracting indices of like bases

$= \frac{a}{c} ^ 2$