Question

A^5/6 * b^7/12 * a^3/4 * b^2/3

Answer 1

A=a?  ⇒a^(5/6+3/4)×b^(7/12+2/3)= a^(19/12)×b^(5/4)

Answer 2

To simplify the expression A^(5/6) * B^(7/12) * A^(3/4) * B^(2/3), we can combine the terms with the same base by adding their exponents. Therefore:

A^(5/6) * B^(7/12) * A^(3/4) * B^(2/3) = A^[(5/6) + (3/4)] * B^[(7/12) + (2/3)]

Let's simplify the exponents:

(5/6) + (3/4) = (10/12) + (9/12) = 19/12

(7/12) + (2/3) = (7/12) + (8/12) = 15/12

Now we have:

A^(5/6) * B^(7/12) * A^(3/4) * B^(2/3) = A^(19/12) * B^(15/12)

To further simplify, we can rewrite the exponents as fractions:

A^(19/12) = (A^(1/12))^19

B^(15/12) = (B^(1/12))^15

Therefore:

A^(5/6) * B^(7/12) * A^(3/4) * B^(2/3) = (A^(1/12))^19 * (B^(1/12))^15

This is the simplified expression.