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Question 1 of 5
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First, separate the numbers and the variables.
Then, bring like terms together.
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2×a×3×b×a×a |
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2×3×a×a×a×b |
Next, using the Product of Powers, bring similar bases together.
Remember that any base without a power means to the power of 1.
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2×3×a×a×a×b |
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= |
21×31×a1×a1×a1×b1 |
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6×a1+1+1×b1 |
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6×a3×b |
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= |
6a3b |
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Question 2 of 5
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First, separate the numbers and the variables.
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5c×d×d×4d×c×d |
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= |
5×c×d×d×4×d×c×d |
Then, bring like terms together.
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5×c×d×d×4×d×c×d |
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= |
5×4×c×c×d×d×d×d |
Next, using the Product of Powers, bring similar bases together.
Remember that any base without a power means to the power of 1.
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5×4×c×c×d×d×d×d |
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= |
51×41×c1×c1×d1×d1×d1×d1 |
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= |
20×c1+1×d1+1+1+1 |
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= |
20×c2×d4 |
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= |
20c2d4 |
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Question 3 of 5
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Notice the bases are the same (y).
Since we are multiplying the bases, add the powers.
Any base without a power means to the power of 1.
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y×y5×y3×y |
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y1×y5×y3×y1 |
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y1+5+3+1 |
Use the Product of Powers |
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= |
y10 |
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Question 4 of 5
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First, separate the numbers and the variables and bring like terms together.
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4m2×3m×m×m3 |
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= |
4×m2×3×m×m×m3 |
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= |
4×3×m2×m×m×m3 |
Next, using the Product of Powers, bring similar bases together.
Remember that any base without a power means to the power of 1.
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4×3×m2×m×m×m3 |
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= |
41×31×m2×m1×m1×m3 |
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= |
12×m2+1+1+3 |
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= |
12×m7 |
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= |
12m7 |
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Question 5 of 5
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Using the Product of Powers, bring similar bases together.
Remember that any base without a power means to the power of 1.
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m×m×m×m×n×nm×n |
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m1×m1×m1×m1×n1×n1m1×n1 |
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= |
m1+1+1+1×n1+1m1×n1 |
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= |
m4×n2m1×n1 |
Simplify further using the Quotient of Powers.
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m4×n2m1×n1 |
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m4m1×n2n1 |
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= |
m4−1×n2−1 |
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m3×n1 |
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= |
m3n |
A power of 1 does not need to be written |