# Simplify ((4y^-3)/(15cy^2))^-2*((8cy)/(3c^2))^2

(4y-315cy2)-2⋅(8cy3c2)2
Move y-3 to the denominator using the negative exponent rule b-n=1bn.
(415cy2y3)-2⋅(8cy3c2)2
Multiply y2 by y3 by adding the exponents.
Move y3.
(415c(y3y2))-2⋅(8cy3c2)2
Use the power rule aman=am+n to combine exponents.
(415cy3+2)-2⋅(8cy3c2)2
(415cy5)-2⋅(8cy3c2)2
(415cy5)-2⋅(8cy3c2)2
Change the sign of the exponent by rewriting the base as its reciprocal.
(15cy54)2⋅(8cy3c2)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 15cy54.
(15cy5)242⋅(8cy3c2)2
Apply the product rule to 15cy5.
(15c)2(y5)242⋅(8cy3c2)2
Apply the product rule to 15c.
152c2(y5)242⋅(8cy3c2)2
152c2(y5)242⋅(8cy3c2)2
Simplify the numerator.
Raise 15 to the power of 2.
225c2(y5)242⋅(8cy3c2)2
Multiply the exponents in (y5)2.
Apply the power rule and multiply exponents, (am)n=amn.
225c2y5⋅242⋅(8cy3c2)2
Multiply 5 by 2.
225c2y1042⋅(8cy3c2)2
225c2y1042⋅(8cy3c2)2
225c2y1042⋅(8cy3c2)2
Reduce the expression by cancelling the common factors.
Raise 4 to the power of 2.
225c2y1016⋅(8cy3c2)2
Cancel the common factor of c and c2.
Factor c out of 8cy.
225c2y1016⋅(c(8y)3c2)2
Cancel the common factors.
Factor c out of 3c2.
225c2y1016⋅(c(8y)c(3c))2
Cancel the common factor.
225c2y1016⋅(c(8y)c(3c))2
Rewrite the expression.
225c2y1016⋅(8y3c)2
225c2y1016⋅(8y3c)2
225c2y1016⋅(8y3c)2
225c2y1016⋅(8y3c)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 8y3c.
225c2y1016⋅(8y)2(3c)2
Apply the product rule to 8y.
225c2y1016⋅82y2(3c)2
Apply the product rule to 3c.
225c2y1016⋅82y232c2
225c2y1016⋅82y232c2
Evaluate the exponents.
Raise 8 to the power of 2.
225c2y1016⋅64y232c2
Raise 3 to the power of 2.
225c2y1016⋅64y29c2
225c2y1016⋅64y29c2
Cancel the common factor of 9c2.
Factor 9c2 out of 225c2y10.
9c2(25y10)16⋅64y29c2
Cancel the common factor.
9c2(25y10)16⋅64y29c2
Rewrite the expression.
25y1016⋅(64y2)
25y1016⋅(64y2)
Cancel the common factor of 16.
Factor 16 out of 64y2.
25y1016⋅(16(4y2))
Cancel the common factor.
25y1016⋅(16(4y2))
Rewrite the expression.
25y10⋅(4y2)
25y10⋅(4y2)
Multiply 4 by 25.
100y10⋅y2
Multiply y10 by y2 by adding the exponents.
Move y2.
100(y2y10)
Use the power rule aman=am+n to combine exponents.
100y2+10
100y12
100y12
Simplify ((4y^-3)/(15cy^2))^-2*((8cy)/(3c^2))^2

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