Multiplication Laws

Exponential: A number written with a power (or exponent), for example 93
Base: The number used as a factor for repeated multiplication (the big number on the bottom)
Power: The number of times the factor is being multiplied, a.k.a. exponent (the number up top)
Simplify: The change to a more simple form (not the same as evaluate or solve!!)

There are laws for simplifying the *multiplication* of exponentials:

1st Multiplication Law: If the exponentials have the same base, the powers can be added: 52 × 53 = 52+3 = 55.

It will be very important for students to see this in proof form, to help them visualize it: 52 × 53 = (5 × 5) × (5 × 5 × 5) = 5 × 5 × 5 × 5 × 5

2nd Multiplication Law: If the exponentials have the same powers, multiply the bases and keep the power: 53 × 63 = (5 × 6)3 = 303