How do you simplify (35a^14 b^6) /( -7a^7 b^3)?

Jan 15, 2016

$- \frac{35 {a}^{7} {b}^{3}}{7}$

Explanation:

To aid understanding I am splitting the fraction into its component parts:

Given: $\frac{35 {a}^{14} {b}^{6}}{- 7 {a}^{7} {b}^{3}}$

Rewrite as: $- \frac{35}{7} \times \frac{{a}^{14}}{{a}^{7}} \times \frac{{b}^{6}}{{b}^{3}}$

$- \frac{35}{7} \times {a}^{14 - 7} \times {b}^{6 - 3}$

$- \frac{35}{7} \times {a}^{7} \times {b}^{3}$

7 is a prime number so it will not divide into 35 'without giving a remainder'. So leave it as it.

Writing the solution in the same form as the question gives

$- \frac{35 {a}^{7} {b}^{3}}{7}$