To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:
Simplify a6 × a5
The rules tell me to add the
exponents. But I when I started algebra, I had trouble keeping the rules
straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together.
Simplifying Expressions
a6 × a5 = (a6)(a5)
= (aaaaaa)(aaaaa)
= aaaaaaaaaaa
= a11
Thus:
a6 × a5 = a11
