# How do you simplify (b^3 a^5)/(b^2 a^4)?

Apr 10, 2016

$\frac{{b}^{3} {a}^{5}}{{b}^{2} {a}^{4}} = b a$

#### Explanation:

$\frac{{b}^{3} {a}^{5}}{{b}^{2} {a}^{4}} = \frac{b \cdot b \cdot b \cdot a \cdot a \cdot a \cdot a \cdot a}{b \cdot b \cdot a \cdot a \cdot a \cdot a}$

So you should cancel b's and a's in nominator and denominator. So the result would be $b \cdot a$.

More scientifically:

$\frac{{b}^{3} {a}^{5}}{{b}^{2} {a}^{4}} = {b}^{3 - 2} \cdot {a}^{5 - 4} = {b}^{1} \cdot {a}^{1} = b \cdot a$

Apr 10, 2016

ab

#### Explanation:

Using the following $\textcolor{b l u e}{\text{ rule of exponents }}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{m} / {a}^{n} \Leftrightarrow {a}^{m - n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{{b}^{3} {a}^{5}}{{b}^{2} {a}^{4}} = {b}^{3} / {b}^{2} \times {a}^{5} / {a}^{4} = {b}^{3 - 2} \times {a}^{5 - 4} = a b$