# Simplify (3x^4y^-5)^3

(3x4y-5)3
Rewrite the expression using the negative exponent rule b-n=1bn.
(3x41y5)3
Multiply 3x41y5.
Combine 3 and 1y5.
(x43y5)3
Combine x4 and 3y5.
(x4⋅3y5)3
(x4⋅3y5)3
Move 3 to the left of x4.
(3⋅x4y5)3
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 3x4y5.
(3×4)3(y5)3
Apply the product rule to 3×4.
33(x4)3(y5)3
33(x4)3(y5)3
Simplify the numerator.
Raise 3 to the power of 3.
27(x4)3(y5)3
Multiply the exponents in (x4)3.
Apply the power rule and multiply exponents, (am)n=amn.
27×4⋅3(y5)3
Multiply 4 by 3.
27×12(y5)3
27×12(y5)3
27×12(y5)3
Multiply the exponents in (y5)3.
Apply the power rule and multiply exponents, (am)n=amn.
27x12y5⋅3
Multiply 5 by 3.
27x12y15
27x12y15
Simplify (3x^4y^-5)^3