Math 017 Materials With Exercises

The above convention can be interpreted as the consequence of the order of operations. For example,2in ( 2x ) parentheses indicate that multiplication should be performed first, and only then the result israised to the second power. This means that the entire 2 x is raised to the second power. Withoutparentheses, we first exponentiate, and then multiply by 2, so only x is squared. Notice also, that22without this convention, we would have no means to distinguish between, let‟s say, 2x and ( 2x ) , or3( a b) and3a b .Example 4.1 Expand, that is write without exponential notation.3a) ( 5A )b) 5ASolution:3a) The exponent pertains to the entire expression 5 A: (5A) 5A5A5Ab) The exponent pertains only to A : 5A3 5AAA .3Example 4.2 Rewrite using exponential notation whenever it is possible.a) 7 mmmb) aaaa aac) b ( c 2d)bb(2d c)bbyd) y yxSolution:a)b7mmm 7m3tomesb) aaaa aa 4times32times a4 ac) Notice that c 2 d 2d c , thus5( c 2d)bb(2d c)bb bbbbb(c 2d)(c 2d) b ( c 2d5times2 2timesyd) Notice that y y is equivalent tox3y yyy y y y x x xyyy , thusx)2Example 4.3 Evaluate a)0( 2x ) b)02x c)4(mn7 ) 0Solution:a) Remember that any expression raised to the zero-th power is equal to 1, andthat because of parentheses the zero power pertains to the entire expression 2 x ,thus (2x)0 1.b) This time only x is raised to the zero-th power, hence 2x 0 21 2.77 0c) The expression m n is raised to the zero-th power, so 4( mn ) 41 439