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Question 1 of 5
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A negative power means we flip a fraction and make the power positive.
[-a2b3]-5 |
= |
[b3−a3]5 |
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= |
b3×5−a2×5 |
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= |
b15-a10 |
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Question 2 of 5
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First, separate the bases..
Now use Negative Powers to simplify the expression.
m−31×n51×1z−4 |
= |
1m3×n51×z41 |
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= |
n5z4m3 |
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Question 3 of 5
Simplify
(10x2y-2)3(2x-1y3)2
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Use Power of a Power and Negative Powers to simplify the expression.
(10x2y−2)3(2x−1y3)2 |
= |
103x2×3y−2×322x−1×2y3×2 |
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= |
1000x6y−64x−2y6 |
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= |
1000x6×x24y6×y6 |
Finally, use the Product of Powers to simplify the expression further.
1000x6×x24y6×y6 |
= |
1000x6+24y6×y6 |
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= |
1000x84y6×y6 |
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= |
1000x84y6+6 |
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= |
250x8y12 |
10004=250 |
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Question 4 of 5
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First, separate the bases.
-3m-2-4m-3 |
= |
(-3-4)(m-2m-3) |
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= |
(34)(m-2m-3) |
Recall, |
Now, use the Quotient of Powers to simplify the expression further.
(34)(m−2m−3) |
= |
(34)(m−2−(−3)) |
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= |
(34)(m−2+3) |
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= |
34m |
A power of 1 does not need to be written |
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Question 5 of 5
Simplify
[35x-2y47x4y-6]-1
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A negative power means we flip a fraction and make the power positive.
[35x-2y47x4y-6]-1 |
= |
[7x4y-635x-2y4]1 |
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= |
7x4y-635x-2y4 |
A power of 1 does not need to be written |
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= |
7x4y−6÷735x−2y4÷7 |
Divide the numerator and denominator by 7 |
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= |
x4y−65x−2y4 |
Now, use the Quotient of Powers to simplify the expression further.
x4y−65x−2y4 |
= |
x4−(−2)y−65y4 |
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= |
x4+2y−65y4 |
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= |
x6y−65y4 |
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= |
x6y−6−45 |
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= |
x6y−6+(−4)5 |
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= |
x6y−105 |
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= |
x65y10 |