. High school algebra . nce a-f = — and a^ = . it follows that any af a~P factor may he removed from the numerator to the denominator of a fraction, or vice versa, by changing the sign of its index. 300 ALGEBRA Thus. -^^ = -^ = 8; -^ = — ; 4x-a3 = -^ . a^/8^x V^IG^; {^^J^ i^Sx VW^ = 8^ X 16* = (23)§ X (2«)^ = 2»x 25=32. 16» 64 / 9a* \g 9 . g- 9»a«6» 27ae6« EXERCISE 189 (1-82. Oral)What is the meaning of: 1. ai 2. xi 3. 1y-. 4. a5. 4 5. a;5. 6. x°. 7. 0-2. 8. a;-^ 9. X-*. 10. y-\ 11. w^ 12. x-l What is the value of: 13. oi 14. lei. 15. 1253. 16. 10,000^ 17. 42. 18. 27^ 19. (i)^. 20.
. High school algebra . nce a-f = — and a^ = . it follows that any af a~P factor may he removed from the numerator to the denominator of a fraction, or vice versa, by changing the sign of its index. 300 ALGEBRA Thus. -^^ = -^ = 8; -^ = — ; 4x-a3 = -^ . a^/8^x V^IG^; {^^J^ i^Sx VW^ = 8^ X 16* = (23)§ X (2«)^ = 2»x 25=32. 16» 64 / 9a* \g 9 . g- 9»a«6» 27ae6« EXERCISE 189 (1-82. Oral)What is the meaning of: 1. ai 2. xi 3. 1y-. 4. a5. 4 5. a;5. 6. x°. 7. 0-2. 8. a;-^ 9. X-*. 10. y-\ 11. w^ 12. x-l What is the value of: 13. oi 14. lei. 15. 1253. 16. 10,000^ 17. 42. 18. 27^ 19. (i)^. 20. 5-2. 21. 10-. 22. 14 2. 23. 8-i 24. (-6)0. 25. 8i 26. (aO)-2. 27. (•25)i 28. (•16)1 29. (|)-2. 30. (-2)-«.>31. 3,) 32. 2^.2-*. ,lj \ 35. :-;.«^36. ^..0i^ Write with positive indices :33. a26-3 >I 34. 2a-3. a Z,//:^^. 38. -V-f 39. |^:^ i^,-_flll ^yx-^y-* x-^y ^ 32/rj 2y Writ© without a denominator: 4x. ?^. 42. ^^. 43. -^. 44. -» fc» 0-26* a«(c+d)-* INDICES 301 Simplify:^* 16 i. 59. Solve a;^=4, a;^=32, x*=27, x^=Z, a;2=8. 215. Operations with Fractional and Negative Indices. The following examples will illustrate how the index laws may beapplied to the multiplication, division, etc., of quantitiesinvolving fractional and negative indices. The work will usually be simplified if all expressions arearranged in descending or ascending powers of some commonletter. Thus, 5+x^+x-^2_^ -i_|_a;2 would be written in descendingpowers of x, thus : Ex. 1.—Multiply 2x^ + 3—x-i by Sx^ —2—5x-i. Ex. 2.—Divide a—b by ah—h^. (1^ (2) 3a;i_2 — ^x^ a — a^b^ &x +9x^- 3 -4x^- 6+ ix^ -10-15x~^ + 5a;-i 8a; +5x^-I9-13«* + 5a;-i -ah^ -b-b 302 ALGEBRA Ex. 3.—Find the square root of —12^*4-10— 9a;-12x* + 10-4a;^+a;-i I 3x^-2 + x^ 9x ^-2 I -12a;^+10 -12x^+ 4 6x^-4 + x^ 6-4x^ + x-^6 —4x ^-j-x^ Verify by squaring 3x^ — 2-\-x ^ by the method of art. 93. Alsocheck by putting a;=l. EXBRCISB 140Multiply: 1.* a;2+3, a;^-2. 2. x+x^
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