# Simplify ((b^(-5/2))/(c^(-2/3)))^2(b^(-1/2)c^(-1/3))^-1

(b-52c-23)2(b-12c-13)-1
Move b-52 to the denominator using the negative exponent rule b-n=1bn.
(1c-23b52)2(b-12c-13)-1
Move c-23 to the numerator using the negative exponent rule 1b-n=bn.
(c23b52)2(b-12c-13)-1
Apply the product rule to c23b52.
(c23)2(b52)2(b-12c-13)-1
Multiply the exponents in (c23)2.
Apply the power rule and multiply exponents, (am)n=amn.
c23⋅2(b52)2(b-12c-13)-1
Multiply 23⋅2.
Combine 23 and 2.
c2⋅23(b52)2(b-12c-13)-1
Multiply 2 by 2.
c43(b52)2(b-12c-13)-1
c43(b52)2(b-12c-13)-1
c43(b52)2(b-12c-13)-1
Multiply the exponents in (b52)2.
Apply the power rule and multiply exponents, (am)n=amn.
c43b52⋅2(b-12c-13)-1
Cancel the common factor of 2.
Cancel the common factor.
c43b52⋅2(b-12c-13)-1
Rewrite the expression.
c43b5(b-12c-13)-1
c43b5(b-12c-13)-1
c43b5(b-12c-13)-1
Rewrite the expression using the negative exponent rule b-n=1bn.
c43b5(1b12c-13)-1
Rewrite the expression using the negative exponent rule b-n=1bn.
c43b5(1b12⋅1c13)-1
Multiply 1b12 and 1c13.
c43b5(1b12c13)-1
Change the sign of the exponent by rewriting the base as its reciprocal.
c43b5(b12c13)
Cancel the common factor of b12.
Factor b12 out of b5.
c43b12b92(b12c13)
Factor b12 out of b12c13.
c43b12b92(b12(c13))
Cancel the common factor.
c43b12b92(b12c13)
Rewrite the expression.
c43b92c13
c43b92c13
Combine c43b92 and c13.
c43c13b92
Multiply c43 by c13 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
c43+13b92
Combine the numerators over the common denominator.
c4+13b92
c53b92
c53b92
Simplify ((b^(-5/2))/(c^(-2/3)))^2(b^(-1/2)c^(-1/3))^-1

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