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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.
(2x23)3×(9x4)12 |
= |
(23×x23×3)×(912×x4×12) |
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= |
8x2×912×x2 |
23×3=2 and 4×12=2 |
Next, use Fractional Powers to simplify the expression further.
8x2×912×x2 |
= |
8x2×(2√9)1×x2 |
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= |
8x2×(3)1×x2 |
2√9=3 |
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= |
8x2×x2×3 |
Rearrange the values |
Finally, simplify further by applying the Product of Powers to the values with the same base.
8x2×x2×3 |
= |
8×3×x2+2 |
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= |
24x4 |
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Question 2 of 5
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First, apply the power of 3 to the top and bottom of the fraction.
(x4y3)3×47x5 |
= |
(x4)3(y3)3×47x5 |
Next, apply the power of a power to the first term.
(x4)3(y3)3×47x5 |
= |
x4×3y3×3×47x5 |
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= |
x12y9×47x5 |
Bring x terms together in one fraction.
Simplify further by applying the Quotient of Powers to the values with the same base.
x12x5×47y9 |
= |
x12−51×47y9 |
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= |
4x77y9 |
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Question 3 of 5
Simplify
(4x14)2÷(64x3)13
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First, apply the power of a power to all terms inside the brackets, then simplify.
(4x14)2÷(64x3)13 |
= |
(42×x14×2)÷(6413×x3×13) |
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= |
(16×x12)÷(4×x1) |
14×2=12 and 3×13=1 |
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= |
16x124x1 |
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= |
4x12x1 |
16÷4=4 |
Simplify further by applying the Quotient of Powers.
Finally, simplify further by applying Negative Powers.
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Question 4 of 5
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First, apply the power of a power to all terms inside the brackets, then simplify.
(a2)−32÷(b−12)3 |
= |
(a2×(−32))÷(b−12×3) |
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= |
a-3÷b-32 |
Simplify further by applying Negative Powers.
Finally, apply Fractional Powers and simplify.
1a3÷1b32 |
= |
1a3÷1(2√b)3 |
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= |
1a3÷1√b3 |
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= |
1a3×√b31 |
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= |
√b3a3 |
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Question 5 of 5
Simplify
(13ab3)2[(-3b)2]3
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First, apply the power of a power to each term in the brackets.
(13ab3)2[(−3b)2]3 |
= |
(13)2×a2×b3×2×(−3b)2×3 |
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= |
19a2b6×(-3b)6 |
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= |
19a2b6×(-3)6b6 |
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= |
(-3)69a2b6b6 |
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= |
7299a2b6b6 |
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= |
81a2b6b6 |
Simplify further by applying the Product of Powers to the values with the same base.
81a2b6b6 |
= |
81a2b6+6 |
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= |
81a2b12 |