Adding, Subtracting and Negative Exponents

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Adding and Subtracting Exponents
Adding and subtracting exponents is very different from multiplying and dividing exponents.  That is, there is no real shortcut to do so.
 
Let's try to add 4² + 4³.  First, we write it out.
 

4² = 4 x 4  and 4³ = 4 x 4 x 4

4 x 4 = 16 and 4 x 4 x 4 = 64

 So, 4²+ 4³ = 16 + 64 = 80.

 We simply do the same for subtraction.

Negative Exponents

We can also raise a base to a negative exponent.  For example, 2 raised to the negative third power is 2(-3).  This is the same as if we had ½³.

 When we have a negative exponent, we make the exponent positive and divide it and the base by 1.

It becomes                        1                     or    1

                                      2 x 2 x 2                      8

Again, any number raised to a negative power becomes 1 over that number to its exponent's positive power.

Much like multiplying and dividing exponents, it is important to write out the long form of the exponent and base in order to add, subtract, and find negative exponents.

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