What does 2^4 actually mean?
Expand the exponent into multiplication to see what it really is.
Equation
y = 3^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 9 |
| 3 | 27 |
| 4 | 81 |
| 5 | 243 |
| 6 | 729 |
What this lesson covers
What you do
You shape the function y = b^x and watch the graph answer.
Challenges to clear
- Set the base b to 2. Look at the table row where x=4. Verify that y=16. This shows that 2^4 means multiplying 2 by itself 4 times (2*2*2*2).
- Two more 2s: check that x = 6 gives 64 (2*2*2*2*2*2).
- Threes this time — slide the base b to 3.
- There is a multiplier in front as well. Slide a until x = 3 reads 54: three 3s make 27, and 54 is two lots of that.
Check yourself
Why is 2^4 not equal to 2*4?
If you set the base b=3 and look at x=3 in the table, what value will y have?
- Because 2^4 means 2*2*2*2 (repeated multiplication), while 2*4 means 2+2+2+2 (repeated addition). — correct
- Because exponents always result in larger numbers than multiplication.
- Because 2*4 is the same as 2^2.
- Because you cannot multiply a base by its exponent.
- 9
- 27 — correct
- 6
- 81