Final Notes Exponents Notes 4b5 4 is the coefficient. The coefficient is any number in front of the variable. The coefficient is multiplied by the variable. b is the base. The base can either be a variable or a number. 5 is the exponent. The exponent is small and is at the top right hand corner of the base. What does 4b5 mean? It is a term and it means 4 · b · b · b · b · b. In other words, the 4 is multiplied by b which is multiplied by 5 times, or the number the exponent is represented. What if the base is a number? 36 = 3 · 3 · 3 · 3 · 3 · 3. Just remember, the exponent tells you how many times to multiply the base. How do exponents work? We can add them! The base HAS to be the same in order to simplify. Example X3 · x 4 means, x · x · x · x· x · x · x = x7. In other words, you can add the exponents even though it’s actually multiplication. Try this one: Y9 · y6 = yes, we can write all of the y’s out, but we can just add the exponents and the final answer is y15. We cannot combine different bases!! x4 · y4 … Our final answer would just be x4y4. We cannot combine two different bases. What if you have coefficients? 2x3 · 6x2 = We will need to multiply the coefficients and add the exponents. The base stays the same… 2 · x · x · x · 6 · x · x = Rearrange the terms so that the numbers and the letters are next to each other… 2· 6 · x · x · x · x · x = 12x5 Final Notes Exponents can also be divided: 𝑥4 𝑥3 = 4 – 3 =1 , or x. How? 𝑥𝑥𝑥𝑥 𝑥𝑥𝑥 = if you cancel the x’s that are on the top and the bottom, you would have an x left over at the top. Do we ever multiply exponents? Yes, when there is a parenthesis. (x4)3 = means x4 · x4 · x4, because the exponent states how many times you multiply everything in the parenthesis. Squares and Square Roots and Cube Roots This is a square. Each side is measured the same distance. If the length is 4, then the width, or height is 4. The area of a square is l x w, or 4 x 4 = 16. Therefore, the square root of 16 (√16) is 4. Remember, the square root HAS to be the same number x itself. Just like 4 x 4 = 16, another way is 42. 𝟑 Cube root looks like this: √𝟏𝟐𝟓 or, 5 x 5 x 5. It is helpful to memorize your squares to 12 and your cube roots.