Using 2 to the x........and feeding it complex numbers.......gives me interesting results.....

henever you multiply two terms with the same base, you can add the exponents:

( x m ) ( x n ) = x( m + n )

However, we can NOT simplify (x4)(y3), because the bases are different: (x4)(y3) = x‍x‍x‍xyyy = (x4)(y3). Nothing combines.

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• Simplify (a5 b3) (a b7).

Now that I know the rule (namely, that I can add the powers on the same base), I can start by moving the bases around to get all the same bases next to each other:

(a5 b3) (a b7) = (a5) (a) (b3) (b7)

Now I want to add the powers on the a's and the b's. However, the second a doesn't seem to have a power. What do I add for this term?

Anything that has no power on it, in a technical sense, being "raised to the power 1". Anything to the power 1 is just itself, since it's "multiplying one copy" of itself. So the expression above can be rewritten as:

(a5) (a) (b3) (b7) = (a5) (a1) (b3) (b7)