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Exponents

Exponents. An exponent is the number of times the base is multiplied by itself. Example 27 can also be written as 3 This means 3 X 3 X 3. 3. Substituting variables for numbers. We can also use variables such as X and Y when using exponents. We can define X and Y as integers.

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Exponents

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  1. Exponents An exponent is the number of times the base is multiplied by itself. Example 27 can also be written as 3 This means 3 X 3 X 3 3

  2. Substituting variables for numbers • We can also use variables such as X and Y when using exponents. We can define X and Y as integers. • For example: 3 = 3 X 3 X 3 = 27 SO: X = (X)(X)(X) 3 3

  3. Variable • A variable is a symbol for a number we don’t know yet like X or Y.

  4. Integers • Integers include zero, positive and negative numbers. They do not include fractions.

  5. Laws of Exponents N X = (X)(X)…..(X) (N factors of X) X = 1 (if X = 0) X X = X -n n 1/N N

  6. Practice 3 • Write 11 as multiplication. • Write u as a fraction using only positive exponents. • What is the value of 100 ? • Evaluate -5 and (-5) -7 1/2 -2 -2

  7. Solutions • 11 X 11 X 11 = 1331 • 1 u • 10 • 1 25 7

  8. Multiplying Exponents • Same base • (X ) (X) = X • Be careful I can add the exponents, because X is the base both time. If I had X and Y I could only combine in the exponents were the same. 5 6 11

  9. DifferencesMath is a language 3 3 3 • (4x) means (4 ) (X ) • 4x means 4 (X)(X)(X) 3

  10. Dividing Exponents 8 6 Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X 8 6 2 8 -6

  11. Dividing Exponents 8 6 Step 1: X X = Step 2: (XX) (XXXXXX) (XXXXXX) STEP 3: (XX) (XXXXXX) (XXXXXX) Step 3: (XX) = X 2

  12. x 0 • Anything divided by itself is 1. X to the zero power is 1. • Example X / X = (X ) (X ) = 1 • This works in all cases except for if X is equal to zero. 3 -3 3 3

  13. Practice Solve: • X X 2) X X = If X = 5 3) X X 4) X X = If X =3 3 2 2 0 -2 -2 4 7

  14. Practice • Solve: • n = 3 729 If x = 64 solve x n = 2 3 n

  15. Practice 3 • Write 12 as multiplication. • Write u as a fraction using only positive exponents. • What is the value of 125 ? • Evaluate -4 and (-4) -5 1/3 -2 -2

  16. Distributive Property The Distributive Property of multiplication is the property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. The Distributive Property says that if a, b and c are real numbers, then a(b + c) = (a x b) + (a x c)

  17. Examples of Distributive property 36 + 8 = 44 Step 1 4 (9 + 2) = Step 2 (4 x 9) + (4 x 2) = Answer 36 + 8 = 44

  18. Practice • 5 (x + 3) 2) x ( y + 9) Are these equal? 3) 25 + 10 = 7 (5 + 0) = 4) 5 + 3 = 20 (3 + 1) = 2

  19. Scientific Notation 4 Definition: A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. Example: The Scientific Notation for 10,492 is 1.0492 X 10 . Show You Tube Video

  20. Practice Convert to Scientific notation • 7535 2) .0027 3) .00045 4) 8,456

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