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Exponents & Order of Operations Repeated Addition problems transform into multiplication problems Example: 3+3+3+3+3= 15 But that takes so long to write out doesn’t it? It is for this reason, multiplication was introduced. So the same addition problems becomes 3 x5= 15 We use multiplication for repeated addition problems because it makes them easier to write and solve. Repeated multiplication becomes… 2x2x2x2x2= This problem can be simplified using a short hand way to write a repeated multiplication problem called EXPONENTS. 2x2x2x2x2= What are the parts of an expression with an exponent? Power 5 2 Exponent Base So this expression means 2 raised to the 5th power How do we solve an expression with an exponent? 5 2 First we need to remember that the exponent tells us how many times to multiply the base number as a factor. So 25 really means 2 x 2 x 2 x 2 x 2 How do we solve an expression with an exponent? 5 2 A common misconception is to think that we solve exponents the same way we do regular multiplication problems. 25 does not mean 2x5 How do we solve an expression with an exponent? 5 2 (exponent in expanded form) 2x2x2x2x2 In order to solve, we will find the partial product 2x2x2x2x2 4 x 4 x2 16 x 2 = 32 How do we solve an expression with an exponent? 2 = 32 5 Practice problems Write the following with an exponent, THEN solve. 1. 5 × 5 × 5 2. 10 × 10 3. 0.2 × 0.2 × 0.2 4. 8 × 8 × 8 × 8 × 8 5. 3 × 3 × 3 × 3 × 3 × 3 × 3 6. 1/ 4 × 1/4 × 1/4 7. 2 × 2 × 2 × 2 × 2 × 2 × 2 8. 6.5 × 6.5 Practice problems Write each power as a product of the same factor. Then find the value. 1. 35 2. 122 3. 63 4. 48 5. (1/2) 3 6. 26 7. 5.43 8. 6.92 Order of Operation P.E.M.D.A.S In your groups, solve this expression. Be ready to post your answer and work on the board and explain and defend the steps you used to solve it. 3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2= What does it mean? Please Excuse My Dear Aunt Sally Purple Elephants Might Destroy A School P.E.M.D.A.S. is a mnemonic device we use to help us remember the order of operations when solving expressions Each letter stands for a type of operationBasically when you are solving an expression if it isn’t a letter or number, it is an operation. {} [] () 𝑟 2 x ÷ + P.E.M.D.A.S helps us to remember what order we complete the operations in expression. What does it REALLY mean? P = Parenthesis or any type of grouping symbols () {} [] What does it REALLY mean? E= Exponents 6 2 2 10 4 8 What does it REALLY mean? Multiply & Divide 4x5 or 10 ÷ 2 Always complete left to right What does it REALLY mean? Add & Subtract 4 + 5 or 10 - 2 Always complete left to right In your groups, you solved this question: 3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2= Review your work and make any changes you would like…… 3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2= 5 3+ 2 -4÷2 3 + 32 - 2 35 – 2 = 33 39 × (15 ÷ 3) – 16 (3 + 7) × 6 + 4 48 ÷ 8 + 5 × (7 – 2) 64 ÷ (15 – 7) × 2 – 9 13 × 4 – 72 8 100 2 5 × 3 4 3 4 – 24 8 5 × 6 – (9 – 4) 4× 2 (5 – 12) – 6 13 + 3 (4 ÷ 2) × 5 – 17 34 – 2 8 ÷4 78 – 4 2 ÷ (14 – 6) × 2