Example

Simplifying 12(โˆ’9)รท(โˆ’3)312(-9) \div (-3)^3

To simplify an expression involving exponents, multiplication, and division with integers, follow the order of operations by resolving exponents prior to performing multiplication or division:

  1. Exponents first: Evaluate (โˆ’3)3=(โˆ’3)(โˆ’3)(โˆ’3)=โˆ’27(-3)^3 = (-3)(-3)(-3) = -27. Since the base is negative and the exponent is odd, the result is negative. The expression becomes 12(โˆ’9)รท(โˆ’27)12(-9) \div (-27).
  2. Multiply: Perform multiplication moving from left to right. Compute 12(โˆ’9)=โˆ’10812(-9) = -108 (multiplying numbers with different signs results in a negative product). The expression becomes โˆ’108รท(โˆ’27)-108 \div (-27).
  3. Divide: Finally, compute โˆ’108รท(โˆ’27)=4-108 \div (-27) = 4 (dividing numbers with the same signs yields a positive quotient).

The final result is 44. This example reinforces that exponents are resolved first, followed by multiplication and division executed sequentially from left to right.

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Updated 2026-05-01

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