Exponents & Powers • Topic 2 of 2

Negative Bases & Order of Operations

Negative bases with exponents: Parentheses make a critical difference!

ExpressionMeaningResult
(-2)^4(-2) x (-2) x (-2) x (-2)+16 (positive)
-2^4-(2 x 2 x 2 x 2)-16 (negative)

Key rule: Even exponent on a negative base gives a positive result. Odd exponent on a negative base gives a negative result.

Order of Operations (PEMDAS):

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (left to right)
  4. Addition and Subtraction (left to right)
ORDER OF OPERATIONS PYRAMID:

        [Parentheses]    (highest priority)
        [Exponents    ]
        [x or /       ]
        [+ or -       ]  (lowest priority)

NEGATIVE BASE RULE:
  Even exponent: (-3)^4 = +81  (positive)
  Odd exponent:  (-3)^3 = -27  (negative)
Solved Examples
1
Worked Example
Evaluate: (-3)^3 vs -3^3
Solution(-3)^3 = (-3) x (-3) x (-3) = -27. Also -3^3 = -(3x3x3) = -27. Same result because exponent is odd.
2
Worked Example
Evaluate: 3 + 4^2 x 2
SolutionExponents first: 4^2=16. Then multiply: 16 x 2=32. Then add: 3+32=35.
3
Worked Example
Evaluate: (-2)^4 - 3^2
Solution(-2)^4 = 16, 3^2 = 9. Result: 16 - 9 = 7.

Key Points

  • Even exponent on negative base gives positive result
  • Odd exponent on negative base gives negative result
  • Parentheses change the meaning: (-2)^4 is different from -2^4
  • Always apply PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.$(-2)^2=$
Explanation: Even power $\to$ positive.
Q2.$(-2)^3=$
Explanation: Odd power $\to$ negative.
Q3.$-3^2=$
Explanation: Power applies before the sign.
Q4.The order of operations does ___ before addition.
Explanation: BODMAS.
Practice more MCQs → 📝 Assignment · 35 marks