1. Review of Exponents, Squares, Square Roots, and Pythagorean Theorem is (repeated Multiplication) written with a base and exponent. Exponential form is (repeated Multiplication) written with a base and exponent. Power is the number produced by raising a base to an exponent. Example: Power is the number produced by raising a base to an exponent. Example:3 5 and 243 represent the same power 3 5 =3·3·3·3·3=243 base exponent

2. ****Pay attention to your rules **** for multiplying negative numbers when you have a negative base. -6 3 = -6 * -6 * -6 36 * -6 = -216 36 * -6 = -216 Try the following: write in expanded form and solve expanded form and solve 5 4= - 12 3= -78 +2(3 3 -15)= 7 1= - 6n 2 = If the volume of a cube is V=s 3 and s is the side, what is the volume of a cube if the side is 8 cm? 7 1= - 6n 2 = If the volume of a cube is V=s 3 and s is the side, what is the volume of a cube if the side is 8 cm? Operations with exponents SOLVE THE ORDER OF OPERATIONS AND THE MEASUREMENT QUESTIONS BELOW

3. Zero and Negative exponents Zero Power- any base with an exponent is of zero (except when the base is zero) is equal to one. 10 0 = 1 Zero Power- any base with an exponent is of zero (except when the base is zero) is equal to one. 10 0 = 1 Negative exponents- any base with a negative exponent is equal to its reciprocal with the opposite exponent 8 -2 = (⅛) 2 = 1/64 Negative exponents- any base with a negative exponent is equal to its reciprocal with the opposite exponent 8 -2 = (⅛) 2 = 1/64 TRY: 7 0 +2 4 +3 -2 = TRY: 7 0 +2 4 +3 -2 =

4. Properties of Exponents When multiplying exponents with the same base, you keep the base and add the exponents. When multiplying exponents with the same base, you keep the base and add the exponents. Example: =6 3 * 6 4 = 6 3+4 =6 7 =279,936 Example: =6 3 * 6 4 = 6 3+4 =6 7 =279,936 When dividing exponents with the same base, keep the base and subtract the exponents. When dividing exponents with the same base, keep the base and subtract the exponents. Example: n 6 /n 4 = n 6-4 = n 2 Example: n 6 /n 4 = n 6-4 = n 2 When raising a power to another power, keep the base and multiply the exponents. When raising a power to another power, keep the base and multiply the exponents. Example (-5 2 ) 3 =-5 2*3 = -5 6 =15,625 Example (-5 2 ) 3 =-5 2*3 = -5 6 =15,625 TRY IT: (x 3 )(x 4 ) (7 3 )(7 2 ) m 10 m 4 ( 2 4 ) 2

5. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros. REMEMBER: YOU MUST HAVE A NUMBER THAT IS GREATER THAN OR EQUAL TO ONE AND LESS THAN TEN, WHEN WRITING IN SCIENTIFIC NOTATION

6. The Distance From the Sun to the Earth 93,000,000 STEP 1: Move decimal left Leave only one number in front of decimal Write number without zeros Step 2: Step 3: Count how many places you moved decimal Make that your power of ten ****The power of ten is 7 because the decimal moved 7 places.

7. Scientific Notation can also be used for very small numbers Scientific Notation can also be used for very small numbers For example: For example: 0.0000000231 can be written in scientific notation with a negative exponent : 0.0000000231 can be written in scientific notation with a negative exponent : 2.31 x 10 -8

8. Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten.

9. Square Roots Square Roots One of the two equal factors of a number. One of the two equal factors of a number. A square root of 144 is ±12 since 12 = 144. A square root of 144 is ±12 since 12 2 = 144. The symbol of square root is a radical √ The symbol of square root is a radical √ The number under the radical is the radicand The number under the radical is the radicand

10. Square Roots Perfect squares Perfect squares Non perfect squares radicands will fall between the square roots of the perfect squares on the number line. Non perfect squares radicands will fall between the square roots of the perfect squares on the number line. √ 1=1 √ 4=2 √ 9=3 √ 16=4 √ 25=5 √ 36=6 √ 49=7 √ 64=8 √ 81=9 √ 100=10 √14 is between the two perfect squares of 3 and 4 √14~ 3.74 ~ √9 √16 3 4 √14

11. TRY IT SOLVE when the square root is not perfect, estimate the square root √36= -√40= √64= √7= √1.69= √400= √18= - √82= √2.25=

12. REAL NUMBERS Rational Numbers are numbers that can be written as a fraction. Their decimal either terminates or repeats. Rational Numbers are numbers that can be written as a fraction. Their decimal either terminates or repeats. Irrational numbers are numbers that cannot be written as a fraction. They do not terminate or repeat Irrational numbers are numbers that cannot be written as a fraction. They do not terminate or repeat If a whole number that is under a radical is not a perfect square, the square root will be irrational. If a whole number that is under a radical is not a perfect square, the square root will be irrational.

13. Irrational and Rational Numbers are Real Numbers. Real Irrationals Rationals 0 1 4 9 16 25 36 49 64 81 100 Perfect squares

14. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. leg hypotenuse right angle

15. The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a 2 + b 2 = c 2. Note: The hypotenuse, c, is always the longest side.

16. Find the length of the hypotenuse if 1. a = 12 and b = 16. Find the length of the hypotenuse if 1. a = 12 and b = 16. 12 2 + 16 2 = c 2 144 + 256 = c 2 400 = c 2 Take the square root of both sides. 20 = c

17. Find the length of the hypotenuse given a = 6 and b = 12 1. 180 2. 324 3. 13.42 4. 18

18. Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10. 4 2 + b 2 = 10 2 16 + b 2 = 100 Solve for b. 16 - 16 + b 2 = 100 - 16 b 2 = 84 b = 9.17

19. Review PowerPoint of Simplifying Radicals Simplifying Radicals.ppt Simplifying Radicals.ppt