Hi Kristine.
There are two key ideas to learn here. The first is that when multiplying numbers with the same base,
you add their exponents. For the first question, this means that you
multiply the scalars together, multiply the a terms by adding
their exponents, and do the same with the b terms:
(5a^{1}b^{7})(2a^{4}b^{2}) =
10a^{1 + 4}b^{7 + 2} =
10a^{3}b^{5}
.
The second key idea is derived from the first one: a negative exponent
is the same as dividing by the positive value. When you are dividing two
quantities with the same base, say c, you subtract their
exponents:
c^{6} c^{2} = c^{4}
.
This means that to turn your negative exponents into positive ones, you make your
answer a fraction with those term(s) in the denominator:
Use the same principle to solve the second question, Kristine.
Hope this helps, Stephen La Rocque.
