simplify: (31/16)^3/4 * [(25/9)^3/2 / (5/2)^-3]

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Solution

31 is not correct since 31 is not 4th power of any number.

(81÷16)^(3÷4) {(25÷9)^(3÷2) ÷ (5÷2)^-3 }

(81÷16)^(3÷4)=(3÷2)^3
=27÷8

(25÷9)^(3÷2)=(5÷3)^3
=125 ÷ 27

(5÷2)^-3 = (2÷5)^3
=8÷125

so what we needed is

(27÷8) × [(125÷27)÷(8÷125)]
=(27÷8)× (125÷27)×(125÷8)
=125 ×125 ÷(8×8)
= (5^3)^2 ÷ (2^3)^2
=((5÷2)^3)^2.

is the answer.

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