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Powers and Indices

Powers and Indices. Slideshow 10, Mathematics Mr Richard Sasaki, Room 307. Objectives. To recall simple algebraic rules To learn how products of an unknown make a power To learn how to multiply and divide powers of an unknown. Review.

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Powers and Indices

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  1. Powers and Indices Slideshow 10, Mathematics Mr Richard Sasaki, Room 307

  2. Objectives • To recall simple algebraic rules • To learn how products of an unknown make a power • To learn how to multiply and divide powers of an unknown

  3. Review Let’s have a review over the algebraic rules we have learned so far with some extra clarifications. = = = = = = = = =

  4. Powers (Indices) What happens when we multiply x by x? = Yes, we get x2. This is read as x-squared or x to the power 2 (or x to the 2). As you can gather, 2, the small number at the top is called the power or the index. (Power and index mean the same thing. Indices is plural for index, we don’t say indexes in this way.)

  5. x1 only involves one x so we just write x. Powers (Indices) = What happens when we multiply x by x by x? = Yes, we get x3. This is read as x-cubed or x to the power 3 (or x to the 3). What happens when we multiply x by x by x by x? = Here we get x4. We can only read this as x to the power 4 (or x to the 4). Other powers are also read “to the power”.

  6. Powers (Indices) Let’s try multiplying a power with another. Simplify a2 x a3. (a × a)×(a × a × a) a2× a3 = a × a × a× a× a = a5 = So… x

  7. Division works in the opposite way. Example Simplify a4 ÷ a2. ÷ a x a x a x a a4÷ a2 = a x a = a2 So when we multiply powers of the same term, the power is added and when we divide, the power is subtracted. Try to remember this!

  8. One more main point here to talk about. What is a0? Have a two minute discussion and try to come up with an idea. If you already know, help explain why. A way to look at it is to work backwards. a0 a1÷ a1 a ÷ a = = = So a0 = 1. =

  9. Let’s try some more complicated examples! Example Simplify 4a4b ÷ 2a2. 4a4b ÷ 2a2 = 2 a2 b Try the last worksheet! Example Simplify 4a4b x 2a2. 4a4b x 2a2 b a6 8 =

  10. Answers 3x2 x3 4y2x y4 x2y2 a7 1 25y2 8x3 x5 x2 y9 x5 x-2 x2 y2 y3 3a2/y2 or 3a2y-2 a 1 2y/x or 2yx-1 4x3 3x2 5y5 x5 6x2 3x7a3 2y2 3a-2 8a3 6x2 6y5 6a2b4

  11. One final thing… Simplify (y4)2… (y4)2 (y4)(y4) = y4 ×y4 = y8 =

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