Worksheet – 4.1-4.2 NAME______________________________
Algebra Review of exponents x m x a x b  x a
 b b x
 h  b x b h  x m
 n x n
1
 x

1 x
If b x  b y x
then x
 y
 x a x
1

2 x b 
3 simplified x
1 x

3 b
0 
1 if b n
  n  x mn x m

0 x m  n
Simplify the following. Express your final answer with positive exponents.
25 p
8
1.
10 p
4 q
2. 4 z 
4
2 z
3. a
4 b

5 b

2 a 7


1
1

 y y


5
3
4.

 x

3
5 x y
4

2


3
5. a

1
1
 b

1

Solve for x :
6. x
2 e
 x 
5 xe
 x 
0
Solve for t without using logarithms:
5
 t
1
7.

2
3 t
4
8. Write a possible exponential function in the form y

Cb x
, with b

0 , b

1 .
b) (0, 5) and (3, 10) c) (-2, 64) and (2, 20.25)
9. If $10,000 is invested at an interest rate of 3% per year, compounded semiannually, find the value of
the investment if it was invested for 4 years.
10. If $10,000 is invested at an interest rate of 3% per year, compounded continuously, find the value of the investment if it was invested for 7 years.