rule
For all numbers x and all integers m and n,
rule1
rule1pic

When you multiply,
and the bases are the same,
you ADD the exponents.

When in doubt, expand the terms (as shown at the right) to see what is happening.

rule1m

rule1m2

Examples:

1.  32 × 34 = 32+4 = 36
The bases are the same (both 3's), so the exponents are added.
2.  22(23) (25) = 22+3+5 = 210
The bases are the same (all 2's), so the exponents are added.

3.  x3x5x6 = x3+5+6 = x14
The bases are the same (all x's), so the exponents are added.

4.  32 + 34 ≠ 32+4
Oops!! This problem is NOT multiplication. This rule does not apply to addition.

5.  5a2 • 2a3a4 = 5 • 2 • 1 • a2+3+4
      = 10a9
The bases are the same (all a's), so the exponents are added. Notice how the numbers in front of the bases (5, 2, and 1) are being multiplied.
6.  3x2 (2x3 + 4) = 3x2 (2x3) + 3x2 (4)
      = 6x5 + 12x2
The
distributive property is applied in this problem. (Multiply each term inside the parentheses by the 3x2 term.)
Then the exponents in the first portion are added since their bases are the same. The numbers in front (the coefficients) are multiplied.
Remember that you cannot add 6x5 and 12x2 since they are not similar (like) terms.

 

divider

NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
and is not considered "fair use" for educators. Please read the "Terms of Use".