# How do you simplify the expression (42a^5b^6)/(7a^2b^3)?

##### 1 Answer
Jun 1, 2016

$6 {a}^{3} {b}^{3}$

#### Explanation:

The first simplification we can make involves the big numbers 42 and 7. Notice that 42 is a multiple of 7:

$\frac{42}{7} = 6$, therefore the fraction can be changed to (6a^5b^6)/(a^2b^3.

Next, let's simplify those exponents. The rule is simple, and it's called the quotient of powers property:

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

This property only works with powers that have the same base. Therefore, we can subtract the powers of the upper and lower letters that are the same:

$6 {a}^{5 - 2} {b}^{6 - 3} = 6 {a}^{3} {b}^{3}$.