 Multiplying Powers MathBitsNotebook.com  For all numbers x and all integers m and n,  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.  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.  x3 • x5 • x6 = 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 • 2a3 • a4 = 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. 