# How do you simplify (3a^7 - a^5 + 5a^3)/(a^2)?

May 26, 2015

You can factor out what's multiplying all the terms in the numerator:

$\frac{{a}^{3} \left(3 {a}^{4} - {a}^{2} + 5\right)}{a} ^ 2$

We can verify this is correct using the property that states ${a}^{n} \cdot {a}^{m} = {a}^{n + m}$.

Then, we can cancel the denominator using the following property:

${a}^{n} / {a}^{m} = {a}^{n - m}$

$\frac{{a}^{\cancel{3}} \left(3 {a}^{4} - {a}^{2} + 5\right)}{\cancel{{a}^{2}}} = a \left(3 {a}^{4} - {a}^{2} + 5\right)$