Ask a New Question
Menu

Evaluate the expression.

12÷(4.5−∣∣−212+2∣∣)⋅(−3)2

1 answer

To evaluate the expression \( 12 \div (4.5 - \lvert -212 + 2 \rvert) \cdot (-3)^2 \), we will follow the order of operations (PEMDAS/BODMAS).

  1. Calculate the absolute value: \[ -212 + 2 = -210 \] Taking the absolute value: \[ \lvert -210 \rvert = 210 \]

  2. Substitute this value back into the expression: \[ 12 \div (4.5 - 210) \cdot (-3)^2 \]

  3. Now calculate \( 4.5 - 210 \): \[ 4.5 - 210 = -205.5 \]

  4. Now we can substitute this back into the expression: \[ 12 \div (-205.5) \cdot (-3)^2 \]

  5. Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]

  6. Now substitute this value back into the expression: \[ 12 \div (-205.5) \cdot 9 \]

  7. Evaluate \( 12 \div (-205.5) \): \[ 12 \div (-205.5) \approx -0.0583 \]

  8. Multiply this result by 9: \[ -0.0583 \cdot 9 \approx -0.5247 \]

Thus, the evaluated result of the expression \( 12 \div (4.5 - | -212 + 2 |) \cdot (-3)^2 \) is approximately

\[ \boxed{-0.5247} \]