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Worksheet – 4.1-4.2 NAME______________________________

Algebra Review of exponents

*x a x b*

*x a*

*b b x*

*h*

*b x b h*

1

*x*

If

*b x x*

1

*b y*

then

*x*

*x*

*y x a x*

1

2

*x b*

3

*x m x n*

*x m*

*n x*

*x*

1

3

*n*

*x m n*

*simplified b*

0

1 if

*b*

0

*x mn*

*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*

3

5

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.