Section 1.2 Operations with Real Numbers and Algebraic Expressions 21 The following numbers appear often in algebra. It is beneficial to commit these to memory. Squares Cubes Fourths 12 = 1 62 = 36 112 = 121 13 = 1 14 = 1 22 = 4 72 = 49 122 = 144 23 = 8 24 = 16 32 = 9 82 = 64 132 = 169 33 = 27 34 = 81 42 = 16 92 = 81 142 = 196 43 = 64 44 = 256 52 = 25 102 = 100 152 = 225 53 = 125 54 = 625 63 = 216 Important Facts About Exponents 1. A negative base raised to an even exponent (2, 4, 6, . . .) is positive. (-5)4 = (-5)(-5)(-5)(-5) = 625 2. A negative base raised to an odd exponent (1, 3, 5, . . .) is negative. (-5)3 = (-5)(-5)(-5)=-125 3. If there are parentheses around a negative number raised to an exponent, then the exponent is applied to the negative number. (-b)n = (-b)(-b) . . . (-b) (''')'''* (-b) is a factor n times 4. If a negative sign is in front of an exponential expression, the negative sign indicates that we take the opposite of the value of the exponential expression. In other words, the negative sign is not part of the base of the exponent. -bn = -b · b · b . . . b ('')''* b is a f actor n times Objective 3 Examples Simplify each exponential expression. Problems Solutions 3a. 25 25 = 2 · 2 · 2 · 2 · 2 = 32 3b. a3 4 b 2 a3 4 b 2 = a3 4 ba3 4 b = 9 16 3c. -34 -34 = -(3 · 3 · 3 · 3) = -81 3d. (-3)4 (-3)4 = (-3)(-3)(-3)(-3) = 81 3e. -43 -43 = -(4 · 4 · 4) = -64 3f. (-4)3 (-4)3 = (-4)(-4)(-4)=-64 Student Check 3 Simplify each exponential expression. a. 63 b. a5 2 b 3 c. -26 d. (-2)6 e. -73 f. (-7)3
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above