Question

Can someone simplify
$\frac{12 {a}^{2} {b}^{6} {c}^{5} }{20 {a}^{2} {b}^{8} {c}^{2} }$

Answer 1

$\frac{12 {a}^{2} {b}^{6} {c}^{5} }{20 {a}^{2} {b}^{8} {c}^{2} }$

To begin, we can simplify the coefficients of the numerator and denominator:

$\frac{12 {a}^{2} {b}^{6} {c}^{5} }{20 {a}^{2} {b}^{8} {c}^{2} } = \\ \\ \frac{3 {a}^{2} {b}^{6} {c}^{5} }{5 {a}^{2} {b}^{8} {c}^{2} }$

Next, the a² in both the numerator and denominator will cancel:

$\frac{3 {a}^{2} {b}^{6} {c}^{5} }{5 {a}^{2} {b}^{8} {c}^{2} } = \\ \\ \frac{3 {b}^{6} {c}^{5} }{5 {b}^{8} {c}^{2} }$

After that, we can simplify the b and c in the numerator and denominator.  Keep in mind that dividing numbers with exponents (that have the same base) is the same as subtraction.  For example, $\frac{{b}^{6} }{ {b}^{8}} }= b^{6-8} = b^{-2}= \frac{1}{b^2}$.

$\frac{3 {b}^{6} {c}^{5} }{5 {b}^{8} {c}^{2} } = \\ \\ \frac{3 {c}^{5} }{5 {b}^{2} {c}^{2} } = \\ \\ \frac{3 {c}^{3} }{5 {b}^{2} }$

$\frac{12 {a}^{2} {b}^{6} {c}^{5} }{20 {a}^{2} {b}^{8} {c}^{2} }$ simplifies to $\frac{3 {c}^{3} }{5 {b}^{2} }$.