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Question 1 of 5
Simplify
2a×3b×a×a2a×3b×a×a
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Incorrect
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First, separate the numbers and the variables.
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2a×3b×a×a2a×3b×a×a |
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2×a×3×b×a×a2×a×3×b×a×a |
Then, bring like terms together.
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2×a×3×b×a×a2×a×3×b×a×a |
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2×3×a×a×a×b2×3×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 11.
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2×3×a×a×a×b2×3×a×a×a×b |
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== |
2121××3131××a1a1××a1a1××a1a1××b1b1 |
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== |
6×a1+1+1×b16×a1+1+1×b1 |
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6×a3×b6×a3×b |
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6a3b6a3b |
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Question 2 of 5
Simplify
5c×d×d×4d×c×d5c×d×d×4d×c×d
Incorrect
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First, separate the numbers and the variables.
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5c×d×d×4d×c×d5c×d×d×4d×c×d |
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5×c×d×d×4×d×c×d5×c×d×d×4×d×c×d |
Then, bring like terms together.
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5×c×d×d×4×d×c×d5×c×d×d×4×d×c×d |
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5×4×c×c×d×d×d×d5×4×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 11.
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5×4×c×c×d×d×d×d5×4×c×c×d×d×d×d |
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== |
5151××4141××c1c1××c1c1××d1d1××d1d1××d1d1××d1d1 |
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20×c1+1×d1+1+1+120×c1+1×d1+1+1+1 |
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20×c2×d420×c2×d4 |
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20c2d420c2d4 |
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Question 3 of 5
Simplify
y×y5×y3×yy×y5×y3×y
Incorrect
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Notice the bases are the same (y)(y).
Since we are multiplying the bases, add the powers.
Any base without a power means to the power of 11.
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y×y5×y3×yy×y5×y3×y |
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y1×y5×y3×y1y1×y5×y3×y1 |
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y1+5+3+1y1+5+3+1 |
Use the Product of Powers |
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y10y10 |
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Question 4 of 5
Simplify
4m2×3m×m×m34m2×3m×m×m3
Incorrect
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First, separate the numbers and the variables and bring like terms together.
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4m2×3m×m×m34m2×3m×m×m3 |
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4×m2×3×m×m×m34×m2×3×m×m×m3 |
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4×3×m2×m×m×m34×3×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 11.
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4×3×m2×m×m×m34×3×m2×m×m×m3 |
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== |
4141××3131××m2m2××m1m1××m1m1××m3m3 |
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12×m2+1+1+312×m2+1+1+3 |
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12×m712×m7 |
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12m712m7 |
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Question 5 of 5
Simplify
m×m×m×m×n×nm×nm×m×m×m×n×nm×n
Incorrect
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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 |