🧩 Exponents & Powers
Exponent = how many times the base is multiplied by itself
▶ Play Door 3Writing Repeated Multiplication as Exponents
An exponent tells how many times to multiply a number (the base) by itself.
5 x 5 x 5 = 5³ (read as '5 to the power of 3' or '5 cubed')
TermMeaningExampleBaseThe number being multiplied5ExponentHow many times to multiply3PowerThe whole expression5³ = 125Special cases:
• a^1 = a (any number to power 1 is itself)
• a^0 = 1 (any nonzero number to power 0 is 1)
• 1^n = 1 (one raised to any power is 1)
Worked example
Problem: Write 7 x 7 x 7 x 7 using exponents.
- 7^4 (four 7's multiplied together)
Answer: 7^4 (four 7's multiplied together)
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):
• Parentheses
• Exponents
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)
Worked example
Problem: Evaluate: (-3)³ vs -3³
- (-3)³ = (-3) x (-3) x (-3) = -27.
- Also -3³ = -(3x3x3) = -27.
- Same result because exponent is odd.
Answer: Same result because exponent is odd.