Simplify ((2p^3)^3)/((3p^6)^2)

Math
(2p3)3(3p6)2
Simplify the numerator.
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Apply the product rule to 2p3.
23(p3)3(3p6)2
Raise 2 to the power of 3.
8(p3)3(3p6)2
Multiply the exponents in (p3)3.
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Apply the power rule and multiply exponents, (am)n=amn.
8p3⋅3(3p6)2
Multiply 3 by 3.
8p9(3p6)2
8p9(3p6)2
8p9(3p6)2
Simplify the denominator.
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Apply the product rule to 3p6.
8p932(p6)2
Raise 3 to the power of 2.
8p99(p6)2
Multiply the exponents in (p6)2.
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Apply the power rule and multiply exponents, (am)n=amn.
8p99p6⋅2
Multiply 6 by 2.
8p99p12
8p99p12
8p99p12
Cancel the common factor of p9 and p12.
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Factor p9 out of 8p9.
p9⋅89p12
Cancel the common factors.
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Factor p9 out of 9p12.
p9⋅8p9(9p3)
Cancel the common factor.
p9⋅8p9(9p3)
Rewrite the expression.
89p3
89p3
89p3
Simplify ((2p^3)^3)/((3p^6)^2)

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