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

1 Answer
Jun 1, 2016

Answer:

#6a^3b^3#

Explanation:

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

#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:

#6a^(5-2)b^(6-3)=6a^3b^3#.