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Module 1: Basic Concepts - Exponents - Practice Problems

Exponential Notations

Instructions:

Work these problems on a sheet of paper and check your answers against those provided below.

#1

What is the numerical value of the following expressions?

1. 10^-4
   
2. 10⁴
   
3. 3⁴
   
4. 8^-3
   

Answer: i. 0.0001

Solution:

i. 10^-4 = 1/10 1/10 1/10 1/10 = 0.0001

Answer: ii. 10,000

Solution:

ii. 10⁴ = 10 10 10 10 = 10,000

Answer: iii. 81

Solution:

iii. 3⁴ = 3 3 3 3 = 81

Answer: iv. 0.001953

Solution:

iv. 8^-3 = 1/8 1/8 1/8 = 0.001953

#2

Using your calculator, find values for the following mathematical expressions:

1. 5^1.23
   
2. 8^-3.4
   
3. 0.5^2.5
   
4. 0.003⁴
   
5. 145 ^0.006
   

Answer:

1. 7.24
   
2. 0.00085
   
3. 0.1768
   
4. 8.1 10^-11
   
5. 1.0303

Instructions:

Read the next section in the lesson before working the next set of practice problems.

Practice Problems

Mathematical Operations

Instructions:

Work these problems on a sheet of paper and check your answers against those provided below.

#1

Addition and Subtraction. Simplify the following:

1. 20a² + 0.5b² + 1.6a² + 1.8a³
   

2. 100a^2.1 50a^2.2 50a^2.1

Answer: i. 21.6a² + 0.5b² + 1.8a³

Solution:

Answer: ii. 50a^2.1 50a^2.2

Solution:

#2

Multiplication. Simplify (or solve) the following:>

1. a³ + (a³)(a^2.4)(b³) + 23
   

2. (a²)(b)(3.5a³) (a²)(b³)(4.5a⁴)

3. How many centimeters cubed are in a meter cubed?
   

Answer: i. a³ + (a^5.4)(b³) + 23

Solution:

Answer: ii. 3.5(a⁵)(b) 4.5(a⁶)(b³)

Solution:

Answer: iii. 10⁶ cm³

Solution:

iii. See Figure 1. There are 10² centimeters per meter.

#3

Division. Simplify the following:

Answer: i. a^1.8

Solution:

Answer: ii. 0

Solution:

#4

Exponents. Simplify the following:

1. (y^4.5)² + 23(2r)²
   

2. (a^2.5)^0.136
   

Answer: i. y⁹ + 92r²

Solution:

i. (y^4.5)² + 23(2r)² = y^{(4.5 2)} + 23(4r²) = y⁹ + 92r²

Answer: ii. a^0.34

Solution:

ii. (a^2.5)^0.136 = a^{(2.5 0.136)} = a^0.34

#5

Mixture of Mathematical Operations. Simplify the following:

Answer: i. 8.4x²

Solution:

Answer:

Solution:

#6

Use your calculator to find values for the following exponential expressions:

Answer: i. 11.55

Solution:

Answer: ii. 14.34

Solution:

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