Test 6 : Exponents



Note: in the following problems /N means square root of N. I could not typeset radical signs.

1) What is 3-3 ?     1/33 = 1/27

     Hint:  2-2 = 1/4
     
2) Simplify  (a7b-2) / (b2a8)?
     1/ab4 or  b-4/a      

     Hint:   c2/c3 = 1/c

3) What is  150%  of 641/2 ?   
     1.5 (8) = 12

     Hint:  x1/2 = square root of x.

4) Simplify    /12  +   /75    =   7 /3

     Hint: /20 = 2  /5

5) What is  (20 + 30)3 ?   23 = 8

     Hint:  x0 = 1  for all x = 0.

6)  Simplify    /(8 x2) ?  2 sqrt(2) x

     Hint: take everything that is a perfect square out of the radical.

7)  What is 323/5 ?       8

     Hint:  Take the fifth root of 32, then cube it.

8) What is   4/(16a1/3 / a1/4) ?  
    =
(16a1/3 / a1/4)1/4
    = (16a1/12)1/4
    = 2a1/48   
     Hint:  a1/3 / a1/4  =  a(1/3 – 1/4)   

9) What is  (0.001)-2/3 ?    100

 Hint: Take the cube root of 0.001, then square it.

10)  Arrange these from least to greatest: 
22/3 ,  23/2,  (½)½,  (½)2,  (½)-2
   Answer   
(½)2,  (½)½ , 22/3 ,  23/2 ,  (½)-2 
 Hint:  square root of 2   =  1.414…