# Simplify (((3xy^-5)^3)/((x^-2y^2)^-4))

((3xy-5)3(x-2y2)-4)
Remove parentheses.
(3xy-5)3(x-2y2)-4
Move (x-2y2)-4 to the numerator using the negative exponent rule 1b-n=bn.
(3xy-5)3(x-2y2)4
Rewrite the expression using the negative exponent rule b-n=1bn.
(3x1y5)3(x-2y2)4
Multiply 3x1y5.
Combine 3 and 1y5.
(x3y5)3(x-2y2)4
Combine x and 3y5.
(x⋅3y5)3(x-2y2)4
(x⋅3y5)3(x-2y2)4
Move 3 to the left of x.
(3⋅xy5)3(x-2y2)4
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 3xy5.
(3x)3(y5)3(x-2y2)4
Apply the product rule to 3x.
33×3(y5)3(x-2y2)4
33×3(y5)3(x-2y2)4
Raise 3 to the power of 3.
27×3(y5)3(x-2y2)4
Multiply the exponents in (y5)3.
Apply the power rule and multiply exponents, (am)n=amn.
27x3y5⋅3(x-2y2)4
Multiply 5 by 3.
27x3y15(x-2y2)4
27x3y15(x-2y2)4
Rewrite the expression using the negative exponent rule b-n=1bn.
27x3y15(1x2y2)4
Combine 1×2 and y2.
27x3y15(y2x2)4
Apply basic rules of exponents.
Apply the product rule to y2x2.
27x3y15⋅(y2)4(x2)4
Multiply the exponents in (y2)4.
Apply the power rule and multiply exponents, (am)n=amn.
27x3y15⋅y2⋅4(x2)4
Multiply 2 by 4.
27x3y15⋅y8(x2)4
27x3y15⋅y8(x2)4
Multiply the exponents in (x2)4.
Apply the power rule and multiply exponents, (am)n=amn.
27x3y15⋅y8x2⋅4
Multiply 2 by 4.
27x3y15⋅y8x8
27x3y15⋅y8x8
27x3y15⋅y8x8
Cancel the common factor of x3.
Factor x3 out of 27×3.
x3⋅27y15⋅y8x8
Factor x3 out of x8.
x3⋅27y15⋅y8x3x5
Cancel the common factor.
x3⋅27y15⋅y8x3x5
Rewrite the expression.
27y15⋅y8x5
27y15⋅y8x5
Cancel the common factor of y8.
Factor y8 out of y15.
27y8y7⋅y8x5
Cancel the common factor.
27y8y7⋅y8x5
Rewrite the expression.
27y7⋅1×5
27y7⋅1×5
Multiply 27y7 and 1×5.
27y7x5
Simplify (((3xy^-5)^3)/((x^-2y^2)^-4))

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