Exponents

You can express 2 · 2 · 2 · 2 · 2  as  2 5 . 2 middle dot 2 middle dot 2 middle dot 2 middle dot 2 , as , 2 to the fifth , .  The raised number 5 shows the number of times 2 is used as a factor. The number 2 is the base. The number 5 is the exponent.

Factored Form :   2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 Exponential Form :   2 5 Standard Form :   32 cap factoredcap form . colon 2 dot 2 dot 2 dot 2 dot 2 . cap exponentialcap form . colon , 2 to the fifth . cap standardcap form . colon 32

A number with an exponent of 1 is the number itself: 8 1 = 8 . 8 to the first , equals 8 .

Any number, except 0, with an exponent of 0 is 1 : 5 0 = 1 . 1 colon , 5 to the , equals 1 .

For powers of 10, the exponent tells how many zeros are in the number in standard form.

• 10 1 = 10 10 to the first , equals 10
• 10 3 = 10 · 10 · 10 = 1000 10 cubed , equals 10 middle dot 10 middle dot 10 equals , 1000
• 10 5 = 10 · 10 · 10 · 10 · 10 = 100 , 000 10 to the fifth , equals 10 middle dot 10 middle dot 10 middle dot 10 middle dot 10 equals 100 comma 000

You can use powers of 10 to write numbers in expanded form.

Exercises

Write each expression using exponents.

1. 6 · 6 · 6 · 6 6 middle dot 6 middle dot 6 middle dot 6
2. 7 · 7 · 7 · 7 · 7 7 middle dot 7 middle dot 7 middle dot 7 middle dot 7
3. 5 · 2 · 2 · 2 · 2 5 middle dot 2 middle dot 2 middle dot 2 middle dot 2
4. 3 · 3 · 3 · 3 · 3 · 14 · 14 3 middle dot 3 middle dot 3 middle dot 3 middle dot 3 middle dot 14 middle dot 14
5. 4 · 4 · 3 · 3 · 2 4 middle dot 4 middle dot 3 middle dot 3 middle dot 2
6. 3 · 5 · 5 · 7 · 7 · 7 3 middle dot 5 middle dot 5 middle dot 7 middle dot 7 middle dot 7

Write each number in standard form.

7. 4 3 4 cubed
8. 9 4 9 to the fourth
9. 12 2 12 squared
10. 6 2 · 7 1 6 squared , middle dot , 7 to the first
11. 11 2 · 3 3 11 squared , middle dot , 3 cubed

Write each number in expanded form using powers of 10.

12. 658
13. 1254
14. 7125
15. 83,401
16. 294,863

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