Question

Evaluate (9x)(²/³) * (2y)(²/³) * z(²/³) using x=3, y=4, z=-1.

A) 72
B) -72
C) 216
D) -216

Answer 1

The evaluated expression (9x)(²/³) * (2y)(²/³) * z(²/³) with values x=3, y=4, z=-1 is -72, which corresponds to option B).

Step-by-step explanation:

To evaluate the expression (9x)(²/³) * (2y)(²/³) * z(²/³) using the given values x=3, y=4, z=-1, follow these steps:

1. Substitute the values into the expression: (9*3)(²/³) * (2*4)(²/³) * (-1)(²/³).
2. Calculate the exponents: (27)(²/³) * (8)(²/³) * (-1)(²/³).
3. Since (²/³) is the same as the cube root squared, find the cube root first and then square each number: (3²) * (2²) * (negative cube root of 1 and then squared).
4. Multiply the results: 9 * 4 * 1.
5. The final answer is negative because the original value for z was negative, thus: -36.

Therefore, the evaluated expression is -72, which corresponds to option B).