1. Powers and Exponents

2. A power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

3. Powers and Exponents The exponent tells you how many times to write the base number – then put multiplication signs between the numbers.

4. Powers and Exponents For example: 2 3 Write the base number – 2 – 3 times, and place multiplication symbols between: 2 x 2 x 2 = 8 so:2 3 = 8 ______________________________ 4 4 = 4 x 4 x 4 x 4 = 128

5. Squaring Numbers The most common exponent is 2 – when you have a base number with an exponent of 2, it’s called squaring a number. To square a number, just multiply it times itself. Example: What is 3 squared? 3 Squared = 3 × 3 = 9

6. Squaring Numbers 7 2 = 10 2 = 8 2 = 2 2 = 6 2 = 9 2 = 0 2 =

7. Squaring Numbers 7 2 =7x7 = 49 10 2 =10x10 = 100 8 2 =8x8 = 64 2 2 =2x2 = 4 6 2 =6x6 = 36 9 2 =9x9 = 81 0 2 =0x0 = 0

8. Square Roots The Square Root Symbol/Radical Symbol This is the special symbol that means "square root", it looks like a division sign with a tail, and actually started hundreds of years ago as a dot with a flick upwards. You can read it as “What number times itself equals”.

9. Square Roots You can use the radical symbol like this: (you would say "the square root of 9 equals 3") The square root of 9 is 3, because when 3 is multiplied by itself you get 9.

10. Mostly, you’ll see the “perfect squares” on the GED If you’re asked to find the square root and it’s not a whole number, use the following method:

11. Example: What is the square root of 32? Now, if you have a calculator, you can just punch it in and get the answer using the shift key + the square (x 2 ) button.

12. Example: What is the square root of 32? If you don’t have a calculator, figure out between which two whole numbers the square root must be.

13. Example: What is the square root of 32? 5 2 is 25, which is too little, and 6 2 is 36, which is too much. Therefore, the square root of 32 must be a number between 5 and 6. You won’t get the exact answer, but you can get close.

14. The square root of 40 is between what two whole numbers?

15. 6 2 = 36 and 7 2 = 49, so the square root of 40 is between 6 and 7

16. You should now be able to do the powers and roots practice on page 114 in your book. Next up is Order of Operations