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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(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.
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Use the power rule aman=am+n to combine exponents.
(23)5+0⋅(8116)-2⋅(23)-1(32)-5⋅(23)5⋅((23)5)2
Add 5 and 0.
(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.
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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
Add -1 and 5.
(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.
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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.
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Factor (23)4 out of (23)4(32)5.
(23)4((32)5)(23)5⋅((23)5)2(8116)2
Cancel the common factors.
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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.
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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.
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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.
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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.
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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.
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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.
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Multiply the exponents in (25)2.
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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.
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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.
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Multiply the exponents in (35)2.
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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.
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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.
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Multiply the numerator by the reciprocal of the denominator.
2433289⋅13
Multiply 89⋅13.
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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.
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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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