1. 32 × 34 = 32+4 = 36
The bases are the same (both 3's), so the exponents are added. |
2. 83 × 25 = 29 × 25 = 214
Sneaky one!!! In this problem 8 can be written as 2 cubed, thus creating the same base for both terms..  . You get to apply the Rule twice in this one problem.
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3. x3 • x5 • x6 = x3+5+6 = x14
The bases are the same (all x's), so the exponents are added.
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4. 
Bases are the same, so the exponents are added.
The coefficients of 3 and 1 (numbers in front of the bases) are being multiplied.
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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.
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6. 
Bases are the same, so the exponents are added.
Be careful when adding negative exponents.
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7. 
Be sure to add only the exponents for the bases that are the SAME.
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8. (-5a5)(2a2) + 9a7 = -10a7 + 8a7
= -2a7
In this example, the two terms have the same base and power, making them similar terms which can be added. |
9. 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. |
10. 
By the Distributive Property, rs is multiplied times EACH term inside the parentheses giving:
rs(4r) + rs(2s)
Multiply through.
Add the exponents with same bases within each multiplication.
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