# Simplify ((6c^(5/2)s^5)/(c^4s^(-3/2)))^-2

(6c52s5c4s-32)-2
Move c52 to the denominator using the negative exponent rule bn=1b-n.
(6s5c4s-32c-52)-2
Multiply c4 by c-52 by adding the exponents.
Move c-52.
(6s5c-52c4s-32)-2
Use the power rule aman=am+n to combine exponents.
(6s5c-52+4s-32)-2
To write 4 as a fraction with a common denominator, multiply by 22.
(6s5c-52+4⋅22s-32)-2
Combine 4 and 22.
(6s5c-52+4⋅22s-32)-2
Combine the numerators over the common denominator.
(6s5c-5+4⋅22s-32)-2
Simplify the numerator.
Multiply 4 by 2.
(6s5c-5+82s-32)-2
(6s5c32s-32)-2
(6s5c32s-32)-2
(6s5c32s-32)-2
Move s-32 to the numerator using the negative exponent rule 1b-n=bn.
(6s5s32c32)-2
Multiply s5 by s32 by adding the exponents.
Move s32.
(6(s32s5)c32)-2
Use the power rule aman=am+n to combine exponents.
(6s32+5c32)-2
To write 5 as a fraction with a common denominator, multiply by 22.
(6s32+5⋅22c32)-2
Combine 5 and 22.
(6s32+5⋅22c32)-2
Combine the numerators over the common denominator.
(6s3+5⋅22c32)-2
Simplify the numerator.
Multiply 5 by 2.
(6s3+102c32)-2
(6s132c32)-2
(6s132c32)-2
(6s132c32)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(c326s132)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to c326s132.
(c32)2(6s132)2
Apply the product rule to 6s132.
(c32)262(s132)2
(c32)262(s132)2
Multiply the exponents in (c32)2.
Apply the power rule and multiply exponents, (am)n=amn.
c32⋅262(s132)2
Cancel the common factor of 2.
Cancel the common factor.
c32⋅262(s132)2
Rewrite the expression.
c362(s132)2
c362(s132)2
c362(s132)2
Simplify the denominator.
Raise 6 to the power of 2.
c336(s132)2
Multiply the exponents in (s132)2.
Apply the power rule and multiply exponents, (am)n=amn.
c336s132⋅2
Cancel the common factor of 2.
Cancel the common factor.
c336s132⋅2
Rewrite the expression.
c336s13
c336s13
c336s13
c336s13
Simplify ((6c^(5/2)s^5)/(c^4s^(-3/2)))^-2

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