Math 1 · Unit 7 · Lesson 1 · part 3 of 6
Exponents: the short way to write the multiplying
Writing 2 × 2 × 2 × 2 × 2 gets old.
Exponents: the short way to write the multiplying
Writing 2 × 2 × 2 × 2 × 2 gets old. An exponent is the short way to write repeated multiplying: 25 means five 2s multiplied together, which is 32. The base is the number being multiplied over and over (here 2). The exponent is how many times it is used (here 5). The whole thing, 25, is called a power.
Read it, then count the 2s
23 = 2 × 2 × 2 = 8. Read: two to the third.
32 = 3 × 3 = 9. Read: three to the second, or three squared.
51 = 5. One 5, nothing to multiply it by.
104 = 10 × 10 × 10 × 10 = 10,000.
Not the same as multiplying
23 is 8, not 6. The exponent counts how many 2s, it does not multiply 2 by 3. And 42 is 16, not 8.
Also 23 and 32 are different: 8 and 9. The base and the exponent have different jobs.
Now the doubling table with exponents: day 3 has 23 = 8 people, day 4 has 24 = 16. The rumor on day x has 2x people. That is an exponential function written with a power: the base is the number you multiply by, and the exponent is the number of steps.