Exponents with decimal and fractional bases
Key Notes :
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 |
The exponent tells you how many times to use the base as a factor.
For example:
(a/b)3 = a/b . a/b . a/b
(0.03)2 = 0.03 · 0.03
(0.02)3 = 0.02 · 0.02 · 0.02
(1/2)4 = 1/2 × 1/2 × 1/2 × 1/2
Learn with an example
Evaluate. Write your answer as a fraction or whole number.
(1/2)4 =____
(1/2)4 = 1/2 × 1/2 × 1/2 × 1/2
= 1/2.2.2.2
= 1/16
Evaluate. Write your answer as a decimal or whole number.
(0.03)4 =____
The base is 0.03 and the exponent is 4. Use 0.03 as a factor 4 times.
| (0.03)4 | = | 0.03 · 0.03 · 0.03 · 0.03 |
= 0.00000081
Evaluate. Write your answer as a decimal or whole number.
(0.01)4 =_______
The base is 0.01 and the exponent is 4. Use 0.01 as a factor 4 times.
(0.01)4 = 0.01 · 0.01 · 0.01 · 0.01
= 0.00000001
Let’s practice!🖊️
