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Question 1 of 5
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First, apply the power of a power to all terms inside the brackets, then simplify.
(8b3)2b5 |
= |
(82b3×2)b5 |
|
= |
64b6b5 |
Simplify further by applying the Product of Powers to the values with the same base.
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Question 2 of 5
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First, apply the Power of Zero to the third term.
(3m3)2×m4× z0 |
= |
(3m3)2×m4× 1 |
|
= |
(3m3)2×m4 |
Next, apply the power of a power to the first term.
(3m3)2×m4 |
= |
(32m3×2)×m4 |
|
= |
9m6×m4 |
Simplify further by applying the Product of Powers to the values with the same base.
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Question 3 of 5
Simplify
(-5a2b)3(4a3b5)2
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Apply the power of a power to the first bracket.
(−5a2b)3(4a3b5)2 |
= |
(−53a2×3b3)(4a3b5)2 |
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= |
(-125a6b3)(4a3b5)2 |
Do the same to the second bracket.
(−125a6b3)(4a3b5)2 |
= |
(−125a6b3)(42a3×2b5×2) |
|
= |
(-125a6b3)(16a6b10) |
Simplify further by applying the Product of Powers to the values with the same base.
(−125a6b3)(16a6b10) |
= |
−125×16×a6+6×b3×b10 |
Collect like terms |
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= |
−2000×a12×b3×b10 |
Evaluate the constant |
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= |
−2000×a12×b3+10 |
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= |
−2000×a12×b13 |
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= |
-2000a12b13 |
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Question 4 of 5
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First, collect like terms.
3x3y-2-6xy-5 |
= |
(3-6)(x3x)(y-2y-5) |
Use Quotient of Powers to simplify the fractions.
(3−6)(x3x)(y−2y−5) |
= |
−12(x3−1)(y−2y−5) |
Simplify the fraction |
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|
= |
−12x2(y−2y−5) |
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|
= |
−12x2y−2−(−5) |
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|
= |
-12x2y3 |
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Question 5 of 5
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First, apply the power of 5 to the top and bottom of the fraction.
(x2y)5×12x2 |
= |
(x2)5y5×12x2 |
Next, apply the power of a power to the numerator of the first term.
(x2)5y5×12x2 |
= |
x2×5y5×12x2 |
|
|
= |
x10y5×12x2 |
Bring x terms together in one fraction.
Simplify further by applying the Quotient of Powers to the values with the same base.
x10x2×12y5 |
= |
x10−21×12y5 |
|
= |
x82y5 |