Question

(27^1/2×(1/9)^3/4)^4/3

Answer 1

Ответ:

( 27^1/2 (1/9)^3/4 )^4/3

( (3^3)*(3^-2)^3/4 )^4/3

( 3^3/2 * 3^-3/2 )^4/3

( 1 )^4/3 = 1

Объяснение:

Answer 2

To simplify the expression (27^(1/2) × (1/9)^(3/4))^(4/3), let's break it down step by step:

1. Simplify the exponents inside the parentheses:

   27^(1/2) = √27 = √(3^3) = 3^(3/2) (1/9)^(3/4) = (√(1/9))^3 = (1/3)^3 = 1/27

2. Substitute the simplified exponents back into the expression:

   (3^(3/2) × (1/27))^(4/3)

3. Multiply the terms inside the parentheses:

   (3^(3/2) × 1/27)^(4/3) = (3^(3/2) / 27)^(4/3) = (3^(3/2) / 3^3)^(4/3) = (3^(3/2 - 3))^(4/3) = (3^(-3/2))^(4/3) = 3^(-3/2 × 4/3) = 3^(-2)

4. Evaluate the final exponent:

   3^(-2) = 1 / 3^2 = 1/9

Therefore, the simplified expression is 1/9.