# Evaluate (2/((16/81)^(-3/4)+(9/4)^(-1/2)))^-2

(2(1681)-34+(94)-12)-2
Simplify the denominator.
Change the sign of the exponent by rewriting the base as its reciprocal.
(2(8116)34+(94)-12)-2
Apply the product rule to 8116.
(281341634+(94)-12)-2
Simplify the numerator.
Rewrite 81 as 34.
(2(34)341634+(94)-12)-2
Apply the power rule and multiply exponents, (am)n=amn.
(234(34)1634+(94)-12)-2
Cancel the common factor of 4.
Cancel the common factor.
(234(34)1634+(94)-12)-2
Rewrite the expression.
(2331634+(94)-12)-2
(2331634+(94)-12)-2
Raise 3 to the power of 3.
(2271634+(94)-12)-2
(2271634+(94)-12)-2
Simplify the denominator.
Rewrite 16 as 24.
(227(24)34+(94)-12)-2
Apply the power rule and multiply exponents, (am)n=amn.
(22724(34)+(94)-12)-2
Cancel the common factor of 4.
Cancel the common factor.
(22724(34)+(94)-12)-2
Rewrite the expression.
(22723+(94)-12)-2
(22723+(94)-12)-2
Raise 2 to the power of 3.
(2278+(94)-12)-2
(2278+(94)-12)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(2278+(49)12)-2
Apply the product rule to 49.
(2278+412912)-2
Simplify the numerator.
Rewrite 4 as 22.
(2278+(22)12912)-2
Apply the power rule and multiply exponents, (am)n=amn.
(2278+22(12)912)-2
Cancel the common factor of 2.
Cancel the common factor.
(2278+22(12)912)-2
Rewrite the expression.
(2278+21912)-2
(2278+21912)-2
Evaluate the exponent.
(2278+2912)-2
(2278+2912)-2
Simplify the denominator.
Rewrite 9 as 32.
(2278+2(32)12)-2
Apply the power rule and multiply exponents, (am)n=amn.
(2278+232(12))-2
Cancel the common factor of 2.
Cancel the common factor.
(2278+232(12))-2
Rewrite the expression.
(2278+231)-2
(2278+231)-2
Evaluate the exponent.
(2278+23)-2
(2278+23)-2
To write 278 as a fraction with a common denominator, multiply by 33.
(2278⋅33+23)-2
To write 23 as a fraction with a common denominator, multiply by 88.
(2278⋅33+23⋅88)-2
Write each expression with a common denominator of 24, by multiplying each by an appropriate factor of 1.
Multiply 278 and 33.
(227⋅38⋅3+23⋅88)-2
Multiply 8 by 3.
(227⋅324+23⋅88)-2
Multiply 23 and 88.
(227⋅324+2⋅83⋅8)-2
Multiply 3 by 8.
(227⋅324+2⋅824)-2
(227⋅324+2⋅824)-2
Combine the numerators over the common denominator.
(227⋅3+2⋅824)-2
Simplify the numerator.
Multiply 27 by 3.
(281+2⋅824)-2
Multiply 2 by 8.
(281+1624)-2
(29724)-2
(29724)-2
(29724)-2
Multiply the numerator by the reciprocal of the denominator.
(2(2497))-2
Multiply 2(2497).
Combine 2 and 2497.
(2⋅2497)-2
Multiply 2 by 24.
(4897)-2
(4897)-2
Change the sign of the exponent by rewriting the base as its reciprocal.
(9748)2
Apply the product rule to 9748.
972482
Raise 97 to the power of 2.
9409482
Raise 48 to the power of 2.
94092304
The result can be shown in multiple forms.
Exact Form:
94092304
Decimal Form:
4.08376736…
Mixed Number Form:
41932304
Evaluate (2/((16/81)^(-3/4)+(9/4)^(-1/2)))^-2

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