Exponents with negative bases
Key notes:
Understanding Negative Bases:
Explain that a negative base in an exponent expression means the base itself is negative, like (-2)^3.
Odd and Even Powers:
Discuss how negative bases behave differently with odd and even exponents. For example, (-2)^3 = -8 (odd exponent gives a negative result), but (-2)^2 = 4 (even exponent gives a positive result).
Calculating Values:
Show how to calculate expressions like (-3)^2 or (-4)^3 step by step, emphasizing the importance of parentheses to avoid mistakes.
Rules of Exponents:
Introduce basic rules such as (-a)^n = -(a^n) for odd n and (-a)^n = (a^n) for even n, highlighting the sign change based on the exponent’s parity.
Real-World Examples:
Provide real-world examples where negative exponents might be encountered, like temperatures below zero or debts.
An exponent tells you how many times its base is used as a factor.
Exponents are used to write repeated multiplication.
For example, for a base of 3:
–32 = –(3 · 3) = –9
–33 = –(3 · 3 · 3) = –27
–34 = –(3 · 3 · 3 · 3) = –81
–35 = –(3 · 3 · 3 · 3 · 3) = –243
An exponent tells you how many times its base is used as a factor.
Exponents are used to write repeated multiplication.
For example, for a base of 2:
–22 = –(2 · 2) = –4
–23 = –(2 · 2 · 2) = –8
–24 = –(2 · 2 · 2 · 2) = –16
–25 = –(2 · 2 · 2 · 2 · 2) = –32
An exponent tells you how many times its base is used as a factor.
Exponents are used to write repeated multiplication.
For example, for a base of 4:
–42 = –(4 · 4) = –16
–43 = –(4 · 4 · 4) = –64
–44 = –(4 · 4 · 4 · 4) = –256
–45 = –(4 · 4 · 4 · 4 · 4) = –1,024
Learn with an example
📢 Evaluate. – 32 = _______
The base is 3 (not –3) and the exponent is 2. Use 3 as a factor 2 times. The negative sign stays out in front.
– 32 = – (3 · 3)
= – 9
📢 Evaluate. – 23 = ______
The base is 2 (not –2) and the exponent is 3. Use 2 as a factor 3 times. The negative sign stays out in front.
– 23 = – (2 · 2 · 2)
= – 8
📢 Evaluate. – 12 =
The base is 1 (not –1) and the exponent is 2. Use 1 as a factor 2 times. The negative sign stays out in front.
– 12 = – (1 · 1)
= – 1
let’s practice! 🖊️
