Exponents with negative bases
Key Notes :
Exponents are used to write repeated multiplication.
For example, for a base of –4:
| (-4)2 | = | (-4) · (-4) = 16 |
| (-4)3 | = | (-4) · (-4) · (-4) = -64 |
| (-4)4 | = | (-4) · (-4) · (-4) · (-4) = 256 |
| (-4)5 | = | (-4) · (-4) · (-4) · (-4) · (-4) = -1,024 |
- if the exponent is even the result is positive
- if the exponent is odd the result is negative
Learn with an example
Evaluate.
(-4)3 = ___
The base is –4 and the exponent is 3. Use –4 as a factor 3 times.
(-4)3 = (–4) · (–4) · (–4)
= –64
Evaluate.
-13 = ___
The base is 1 (not –1) and the exponent is 3. Use 1 as a factor 3 times. The negative sign stays out in front.
-13 = –(1 · 1 · 1)
= –1
Evaluate.
(-3)3 =___
The base is –3 and the exponent is 3. Use –3 as a factor 3 times.
(-3)3 = (–3) · (–3) · (–3)
= –27
Let’s practice!🖊️
