# Evaluate ((2/3)^5*(2/3)^0*(81/16)^-2*(2/3)^-1)/((3/2)^-5*(2/3)^5*((2/3)^5)^2)

(23)5⋅(23)0⋅(8116)-2⋅(23)-1(32)-5⋅(23)5⋅((23)5)2
Multiply (23)5 by (23)0 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
(23)5+0⋅(8116)-2⋅(23)-1(32)-5⋅(23)5⋅((23)5)2
(23)5⋅(8116)-2⋅(23)-1(32)-5⋅(23)5⋅((23)5)2
(23)5⋅(8116)-2⋅(23)-1(32)-5⋅(23)5⋅((23)5)2
Multiply (23)5 by (23)-1 by adding the exponents.
Move (23)-1.
(23)-1(23)5⋅(8116)-2(32)-5⋅(23)5⋅((23)5)2
Use the power rule aman=am+n to combine exponents.
(23)-1+5⋅(8116)-2(32)-5⋅(23)5⋅((23)5)2
(23)4⋅(8116)-2(32)-5⋅(23)5⋅((23)5)2
(23)4⋅(8116)-2(32)-5⋅(23)5⋅((23)5)2
Reduce the expression by cancelling the common factors.
Move (8116)-2 to the denominator using the negative exponent rule b-n=1bn.
(23)4(32)-5⋅(23)5⋅((23)5)2(8116)2
Move (32)-5 to the numerator using the negative exponent rule 1b-n=bn.
(23)4(32)5(23)5⋅((23)5)2(8116)2
Cancel the common factor of (23)4 and (23)5.
Factor (23)4 out of (23)4(32)5.
(23)4((32)5)(23)5⋅((23)5)2(8116)2
Cancel the common factors.
Factor (23)4 out of (23)5⋅((23)5)2(8116)2.
(23)4((32)5)(23)4(23⋅((23)5)2(8116)2)
Cancel the common factor.
(23)4(32)5(23)4(23⋅((23)5)2(8116)2)
Rewrite the expression.
(32)523⋅((23)5)2(8116)2
(32)523⋅((23)5)2(8116)2
(32)523⋅((23)5)2(8116)2
(32)523⋅((23)5)2(8116)2
Simplify the numerator.
Apply the product rule to 32.
352523⋅((23)5)2(8116)2
Raise 3 to the power of 5.
2432523⋅((23)5)2(8116)2
Raise 2 to the power of 5.
2433223⋅((23)5)2(8116)2
2433223⋅((23)5)2(8116)2
Simplify the denominator.
Combine 23 and ((23)5)2.
243322((23)5)23(8116)2
Combine 2((23)5)23 and (8116)2.
243322((23)5)2(8116)23
243322((23)5)2(8116)23
Simplify the numerator.
Apply the product rule to 23.
243322(2535)2(8116)23
Apply the product rule to 2535.
243322(25)2(35)2(8116)23
Combine exponents.
Combine 2 and (25)2(35)2.
243322(25)2(35)2(8116)23
Combine 2(25)2(35)2 and (8116)2.
243322(25)2(8116)2(35)23
243322(25)2(8116)2(35)23
Apply the product rule to 8116.
243322(25)2812162(35)23
Combine exponents.
Combine 2 and 812162.
24332(25)22⋅812162(35)23
Combine (25)2 and 2⋅812162.
24332(25)2(2⋅812)162(35)23
24332(25)2(2⋅812)162(35)23
Remove unnecessary parentheses.
24332(25)2⋅2⋅812162(35)23
Multiply the numerator by the reciprocal of the denominator.
24332(25)2⋅2⋅812162⋅1(35)23
Simplify the numerator.
Multiply the exponents in (25)2.
Apply the power rule and multiply exponents, (am)n=amn.
2433225⋅2⋅2⋅812162⋅1(35)23
Multiply 5 by 2.
24332210⋅2⋅812162⋅1(35)23
24332210⋅2⋅812162⋅1(35)23
Raise 2 to the power of 10.
243321024⋅2⋅812162⋅1(35)23
Raise 81 to the power of 2.
243321024⋅2⋅6561162⋅1(35)23
Combine exponents.
Multiply 1024 by 2.
243322048⋅6561162⋅1(35)23
Multiply 2048 by 6561.
2433213436928162⋅1(35)23
2433213436928162⋅1(35)23
2433213436928162⋅1(35)23
Raise 16 to the power of 2.
2433213436928256⋅1(35)23
Divide 13436928 by 256.
24332524881(35)23
Simplify the denominator.
Multiply the exponents in (35)2.
Apply the power rule and multiply exponents, (am)n=amn.
2433252488135⋅23
Multiply 5 by 2.
243325248813103
243325248813103
Raise 3 to the power of 10.
2433252488(159049)3
2433252488(159049)3
Cancel the common factor of 6561.
Factor 6561 out of 52488.
243326561(8)1590493
Factor 6561 out of 59049.
243326561⋅816561⋅93
Cancel the common factor.
243326561⋅816561⋅93
Rewrite the expression.
243328(19)3
243328(19)3
Combine 8 and 19.
24332893
24332893
Simplify the denominator.
Multiply the numerator by the reciprocal of the denominator.
2433289⋅13
Multiply 89⋅13.
Multiply 89 and 13.
2433289⋅3
Multiply 9 by 3.
24332827
24332827
24332827
Multiply the numerator by the reciprocal of the denominator.
24332⋅278
Multiply 24332⋅278.
Multiply 24332 and 278.
243⋅2732⋅8
Multiply 243 by 27.
656132⋅8
Multiply 32 by 8.
6561256
6561256
The result can be shown in multiple forms.
Exact Form:
6561256
Decimal Form:
25.62890625
Mixed Number Form:
25161256
Evaluate ((2/3)^5*(2/3)^0*(81/16)^-2*(2/3)^-1)/((3/2)^-5*(2/3)^5*((2/3)^5)^2)

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