Simplify ((9r^3y^-2*(2r^-4y^3))/(6r^2y))^3

Math
(9r3y-2⋅(2r-4y3)6r2y)3
Multiply r3 by r-4 by adding the exponents.
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Move r-4.
(9(r-4r3)y-2⋅(2y3)6r2y)3
Use the power rule aman=am+n to combine exponents.
(9r-4+3y-2⋅(2y3)6r2y)3
Add -4 and 3.
(9r-1y-2⋅(2y3)6r2y)3
(9r-1y-2⋅(2y3)6r2y)3
Multiply y-2 by y3 by adding the exponents.
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Move y3.
(9r-1(y3y-2)⋅26r2y)3
Use the power rule aman=am+n to combine exponents.
(9r-1y3-2⋅26r2y)3
Subtract 2 from 3.
(9r-1y1⋅26r2y)3
(9r-1y1⋅26r2y)3
Simplify 9r-1y1⋅2.
(9r-1y⋅26r2y)3
Move r-1 to the denominator using the negative exponent rule b-n=1bn.
(9y⋅26r2yr)3
Multiply r2 by r by adding the exponents.
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Move r.
(9y⋅26(r⋅r2)y)3
Multiply r by r2.
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Raise r to the power of 1.
(9y⋅26(r1r2)y)3
Use the power rule aman=am+n to combine exponents.
(9y⋅26r1+2y)3
(9y⋅26r1+2y)3
Add 1 and 2.
(9y⋅26r3y)3
(9y⋅26r3y)3
Cancel the common factor of 9 and 6.
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Factor 3 out of 9y⋅2.
(3(3y⋅2)6r3y)3
Cancel the common factors.
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Factor 3 out of 6r3y.
(3(3y⋅2)3(2r3y))3
Cancel the common factor.
(3(3y⋅2)3(2r3y))3
Rewrite the expression.
(3y⋅22r3y)3
(3y⋅22r3y)3
(3y⋅22r3y)3
Cancel the common factor of y.
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Cancel the common factor.
(3y⋅22r3y)3
Rewrite the expression.
(3⋅22r3)3
(3⋅22r3)3
Cancel the common factor of 2.
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Cancel the common factor.
(3⋅22r3)3
Rewrite the expression.
(3r3)3
(3r3)3
Simplify the expression.
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Apply the product rule to 3r3.
33(r3)3
Raise 3 to the power of 3.
27(r3)3
Multiply the exponents in (r3)3.
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Apply the power rule and multiply exponents, (am)n=amn.
27r3⋅3
Multiply 3 by 3.
27r9
27r9
27r9
Simplify ((9r^3y^-2*(2r^-4y^3))/(6r^2y))^3

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