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

Math
(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.
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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.
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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
Multiply s5 by s32 by adding the exponents.
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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.
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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
Use the power rule (ab)n=anbn to distribute the exponent.
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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.
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Apply the power rule and multiply exponents, (am)n=amn.
c32⋅262(s132)2
Cancel the common factor of 2.
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Cancel the common factor.
c32⋅262(s132)2
Rewrite the expression.
c362(s132)2
c362(s132)2
c362(s132)2
Simplify the denominator.
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Raise 6 to the power of 2.
c336(s132)2
Multiply the exponents in (s132)2.
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Apply the power rule and multiply exponents, (am)n=amn.
c336s132⋅2
Cancel the common factor of 2.
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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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