Unit 3- Powers and Exponents
This unit is about powers, exponents, zero exponents, exponent laws, problem solving using powers, and square roots.
Parts of Powers
Definitions
- POWER- The entire group with base and exponent that tells you how many times to multiply the base. The picture below shows a power.
- EXPONENT-The small number above a base or big number that tells you the amount of times you multiply that big number. I will use this little arrow instead- ^. So an exponent will look like this- 4^3. Normally, the three is very small up by the corner of the four like the picture below.
- Example- In the example above, you multiply the 4 three times. (4 x 4 x 4)
- BASE-The big number at the bottom of the power. That number is the one that is being multiplied.
- Example- In the power 2^4, the base is the 2, so you multiply the 2 four times. (2 x 2 x 2 x 2)
About Bases and Exponents
http://www.mathsisfun.com/definitions/exponent.html
-Example- Label the power below.
![Picture](/uploads/2/8/6/5/28654641/655580.png)
Which number is the Exponent?
Which number is the base?
(Hint-since the numbers are the same, you will always be right.)
Answer-The bottom number is the base, the top number is the exponent.
Which number is the base?
(Hint-since the numbers are the same, you will always be right.)
Answer-The bottom number is the base, the top number is the exponent.
Solving Powers
- When solving powers, think of repeated multiplication.
- Example- 6^2 is 6 x 6. 6 x 6 is 36, so 6^2 is 36.
-Try to solve this- 5^4 Answer-625
- Whenever the exponent of a number is 0, the answer will always be 1. So, 3^0 is 1. 4^0 is 1. 34345878356783478135904576826458769356^0 is...1.
- Example-What is 3^0 Answer-1
Exponent Laws
- Multiplying Exponents-When you are multiplying two positive powers together, you may add the exponents when the bases are the same.
Example- 5^3 x 5^8 is 5^11.
-Try this-6^4 x 6^3 Answer-6^7
- Dividing exponents is much the same, but instead of adding the exponents subtract.
Example-9^4 / 9^2 is 9^2.
-Try this-4^7 / 4^3 Answer-4^4
- This only works with positive exponents.
Negative Exponents
- When you have a negative exponent, remember to switch it around so that the exponent is positive.
Example- 9^-2 turns into 1/9^2. Or, in normal exponents,
Negative Exponents
https://www.freemathhelp.com/negative-exponents.html
Square Roots
- Square roots are numbers that can be multiplied by itself to make a number.
8 x 8 is 64, 7 x 7 is 49 and 6 x 6 is 36.
-Try this- What is the square root of 81? Answer- 9.
-What is the square root of 100? Answer- 10
-Solve the problem below.
Answer- 5.
About Square Roots
http://www.wyzant.com/resources/lessons/math/elementary_math/multiplication/square_roots
About Square Roots
http://www.wyzant.com/resources/lessons/math/elementary_math/multiplication/square_roots