(6c52s5c4s-32)-2

Move c52 to the denominator using the negative exponent rule bn=1b-n.

(6s5c4s-32c-52)-2

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

Add -5 and 8.

(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

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

Add 3 and 10.

(6s132c32)-2

(6s132c32)-2

(6s132c32)-2

Change the sign of the exponent by rewriting the base as its reciprocal.

(c326s132)2

Apply the product rule to c326s132.

(c32)2(6s132)2

Apply the product rule to 6s132.

(c32)262(s132)2

(c32)262(s132)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

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