Question

12^3/4 ×3^9/4 / 4^-1/4

Answer 1

Ответ:        123 / 4 × 39 / 4 / 4−1 / 4 = 2 125 764

Answer 2

To simplify the expression 12^(3/4) × 3^(9/4) / 4^(-1/4), you can use the properties of exponents. Here's how you can do it step by step:

1. First, simplify each term with fractional exponents: 12^(3/4) = (2^2 * 3)^(3/4) = 2^(2*(3/4)) * 3^(3/4) = 2^(3/2) * 3^(3/4)

   3^(9/4) = 3^(2*(9/8)) = (3^(9/8))^2 = (3^(1/2))^2 = 3^(1/2)

   4^(-1/4) = 1 / 4^(1/4) = 1 / (2^(1/2)) = 1 / 2^(1/2)

2. Now, substitute these simplified terms back into the original expression: (2^(3/2) * 3^(3/4)) * (3^(1/2)) / (1 / 2^(1/2))

3. Use the properties of exponents to simplify further: 2^(3/2) * 3^(3/4) * 3^(1/2) * (2^(1/2)) (Note: When multiplying terms with the same base, you can add the exponents)

4. Combine like terms: 2^(3/2 + 1/2) * 3^(3/4 + 1/2)

5. Simplify the exponents: 2^(2) * 3^(5/4)

6. Finally, calculate the values of 2^2 and 3^(5/4): 2^2 = 4 3^(5/4) ≈ 6.0845

So, the simplified expression is: 4 * 6.0845 ≈ 24.3380