Math 017 Materials With Exercises

Lesson 4e) No, we cannot. Even if the expressions have the same answers in a-d, we cannot conclude that the expression willalways be equivalent. f) (−1) m =1, −1 m =−1, when m=2. Yes, we can, they are not equivalent. It is enough to findone set of values of variables for which two expressions are not equal to determine that they are not equivalent.1 coefficient, exponent or power, the base.2 a) first b) zero3 a) b b) ab c) de d) ─a e) a f) 2x y 43 a4 a)2 2 2 b) a c) d) ( 5a ) e) 3 75 base exponent coefficienta) x 4 3b) x m −16 a)3cc) x 323d) a bc2 −1e)xym 1f) x y714g)3x z37w4h) ab 51256 b)i) m+ n 2 +m j)34z c)3 a3 4 d) x5 y 2 e)34k k k k) z z zn n314z28a f)4 a a f)l) x y ( z)3z z z5( x) g)10 x2 2x y xy g)m)xx243 x3( a b) h) n) 2a 3 o) p) q)r) b x3 s) m n)m n( w 2v) m ( m p n)7 a) (−4) (−4) (−4) (−4) (−4) b) −4∙4∙4∙4∙4 c) (−m) (−m) (−m) d) −m∙ m∙ me) ( 2a )(2a)(2a)f) 2 a a ag) ( a b)(a b)h) a b b8 a) 1 b) 3 c) x d) a e) ab f) 1 g) ab 1h) 193a) x4b) ( x) , necessary7c) xd)3, necessarye)( b3a 2 ) , necessary f)3a 2bg)3a )2( 2t3 ) 4( 3 x)2( t) ( n m p)m( bc , necessary h)a ( 2b) 2x y 4, necessary10 a) 2,000,000 b) 8,000,000The answers are different, since the order of operations is different. In part b, we must first complete operations withinparentheses.11 a) To multiply exponential expressions with the same bases one needs to add the exponents.b) To divide exponential expressions with the same bases one needs to subtract their exponentsc) To raise an exponential expression to another power one needs to multiply exponents.12 a)i)23n b)169a j)14s c)12x k)6x d)1 a23 l)28b e)3x m)216x f)326a n)902m g) b h) 115s o)12 5t p)x 1218x3Answers to Exercises 121