Easy Algebra Step-by-Step

32 3 Roots and Radicals In this chapter, you learn about square roots, cube roots, and so on. Additionally, you learn about radi ...

Roots and Radicals 33 A number that is an exact square of another number is a perfect square. For instance, the integers 4, 9, 1 ...

34 Easy Algebra Step-by-Step b.^4 9 Step 1. Find the principal square root of 4 9 . 2 3 2 3 4 9 ⋅=, so 2 3 is the principal squa ...

Roots and Radicals 35 81 ≠± 9. The square root symbol always gives just one nonnegative number as the answer! If you want ± 9 , ...

36 Easy Algebra Step-by-Step f. − 22 ⋅− Step 1. Find the principal square root of − 22 ⋅−. − 22 ⋅− =− 22 = g. bb Step 1. Find th ...

Roots and Radicals 37 (^3) −≠ 27 − 9. You do not divide by 3 to get a cube root. e.^3 − 77 ⋅− ⋅− 7 f.^3 bbbbb Solution a.^3 −^27 ...

38 Easy Algebra Step-by-Step In general, if xxx xa nx xxx⋅⋅x ft f , where n is a natural number, x is called an nth ...

Roots and Radicals 39 (^6) −≠ 11 ≠−. (^) − 111111 ⋅−⋅−⋅−⋅−⋅−= 1 , not − 1. c.^30.^125 Step 1. Find the principal cube root of 0. ...

40 Easy Algebra Step-by-Step c.^3 4 d.^1 2 Solution a. 48 Step 1. Express 48 as a product of two numbers, one of which is the la ...

Roots and Radicals 41 Step 3. Find 36 and put the answer in front of 10 as a coeffi cient. = 610 Step 4. Review the main results ...

42 Easy Algebra Step-by-Step d.^1 2 Step 1. Multiply the numerator and the denominator of 1 2 by the least number that will make ...

Roots and Radicals 43 Exercise 3 For 1–4, fi nd the two square roots of the given number. 144 2.^25 49 3. 0.64 4. 400 For 5–18 ...

44 4 Exponentiation This chapter presents a detailed discussion of exponents. Working effi ciently and accurately with exponents ...

Exponentiation 45 Step 2. Do the multiplication. 35 = 33333333333 = 243 (t he fi fth power of 3) The following discussion tells ...

46 Easy Algebra Step-by-Step of the number; read 53 as “fi ve cubed.” Beyond the third power, read 54 as “fi ve to the fourth,” ...

Exponentiation 47 d.^3 4 ⎛^3 ⎝⎜ ⎛⎛ ⎝⎝ ⎞ ⎠⎟ ⎞⎞ ⎠⎠ e. 0100 f. 13 g. ()^3 Solution a. 25 Step 1. Write 25 in product form. 25 = 222 ...

48 Easy Algebra Step-by-Step Step 2. Do the multiplication. 3 4 3 4 3 4 3 4 27 64 3 ⎛ ⎝ ⎛⎛⎛⎛ ⎝⎝ ⎛⎛⎛⎛ ⎞ ⎠ ⎞⎞⎞⎞ ⎠⎠ ⎞⎞⎞⎞ =⋅⋅= e. 01 ...

Exponentiation 49 Problem Evaluate. a. ()^0 b. (..^6 )^0 c. 3 4 ⎛^0 ⎝⎜ ⎛⎛ ⎝⎝ ⎞ ⎠⎟ ⎞⎞ ⎠⎠ d. ππ^0 e. 10 Solution a. ()^0 Step 1. T ...

50 Easy Algebra Step-by-Step Negative Integer Exponents If x is a nonzero real number and n is a natural number, then x x n n − ...

Exponentiation 51 c. (.. 6 )−^2 Step 1. Write the reciprocal of the corresponding positive exponent version of () 06. −^2. 2 1 ( ...