First, some vocab.

The term

*exponent*refers to the tiny number that sits above and to the right of another number or variable. It denotes the number of times that the big number next to it-- called the base-- should be multiplied by itself. If, for example, we have something like this:

x

^{3}(hereafter written as x^3)

--this means we multiply x times x times x (written as x*x*x). The variable x is the base; 3 is the exponent.

What would 3

^{4}be? (hereafter 3^4)?

Multiply: 3*3*3*3 = 81.

If two exponential expressions have the same base, you can do interesting things with them.

(x^2)*(x^3) = (x^5) Notice that, when you multiply these two quantities, the powers

*add!*The general rule, then, is

(x^a)*(x^b) = x^(a+b)

Example:

(2^2)*(2^4) = (2^6) = 64

CAUTION: Be careful not to confuse an expression like 2^3 with 2*3!! Students often make this mistake. 2 cubed is 8, but 2 times 3 is 6.

How do we know that multiplying exponential expressions with the same bases means adding exponents? We can work it out the long way.

This equation

(x^2)*(x^3) = (x^5)

can be rewritten as

(x*x)*(x*x*x) = x*x*x*x*x (associative property of multiplication)

...which is x^5!

Remember, though, that if the bases are different, you can't multiply two exponential quantities together and expect to add the exponents. Doesn't work.

OK... more later!

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