Learning Objectives

By the end of this lesson, you should be able to:

1. Identify the base and exponent and write repeated multiplication as a power.
2. Evaluate powers and use powers to find the area of a square and the volume of a cube.

Growing Through Repetition

Learning mathematics requires practice. When we repeat a process carefully, we become more confident and accurate. Powers also describe repetition: the same factor is multiplied again and again. This can remind us that small, faithful steps can produce meaningful growth.

Memory verse: “For the LORD gives wisdom; from his mouth come knowledge and understanding.” — Proverbs 2:6

1. What Is a Power?

A power is the result of multiplying the same factor repeatedly. A power has two important parts: a base and an exponent.

• The base is 5. It is the factor being multiplied.
• The exponent is 3. It tells us how many times the base is used as a factor.
• The entire expression, 5³, is called a power.

Important: The expression 5³ means 5 multiplied by itself three times. It does not mean 5 × 3.

2. Reading and Writing Powers

Numbers raised to the first power are usually written without the exponent. For example, 12¹ = 12.

3. Evaluating Powers

To evaluate a power, multiply the base by itself the number of times shown by the exponent.

Special case: Any non-zero number raised to the first power is itself. For example, 7¹ = 7.

4. Using Powers in Geometry

Some formulas use powers to describe areas and volumes.

Area is measured in square units, such as cm². Volume is measured in cubic units, such as cm³.

Practice Questions

Show your working. Try each question before opening the answer sliders.

1. Skill Practice

1. Write each product using an exponent:
   1. 4 × 4 × 4 × 4
   2. 7 × 7
   3. 10 × 10 × 10
   4. x × x × x × x × x
   5. 0.5 × 0.5
2. Write each power as a repeated multiplication:
   1. 3⁴
   2. 6²
   3. a³
   4. 2⁵
3. For each power, state the base and the exponent:
   1. 9³
   2. 12²
   3. b⁵
4. Write each power in words:
   1. 7²
   2. 4³
   3. n⁵
5. Evaluate:
   1. 2⁴
   2. 5³
   3. 10²
   4. 1⁸
   5. 0.5²
6. Evaluate each expression when n = 8 and m = 0.3:
   1. n²
   2. n³
   3. n⁴
   4. m²
   5. m³
7. Complete the table by writing the repeated multiplication and value for each power: 2⁴, 3³, 10², and (0.5)².

2. Applications

8. Square photo frame: A square photo frame has a side length of 9 cm. Use A = s² to find its area.
9. Cube-shaped box: A cube-shaped box has an edge length of 4 m. Use V = s³ to find its volume.
10. Aquarium: An aquarium has a square base with a side length of 15 inches. It is filled with water to a height of 15 inches.
    1. Find the volume of water in the aquarium.
    2. A cubic inch of water weighs approximately 0.036 pounds. Find the approximate weight of the water.
11. Patterns: The sums of the first odd numbers are shown below:

    1 = 1²    1 + 3 = 2²    1 + 3 + 5 = 3²

    1. Write a variable expression for the sum of the first n odd numbers.
    2. Use your expression to find the sum of the first 100 odd numbers.
12. Floor tiles: A square classroom floor has a side length of 12 m. Each square metre can hold one large floor tile. How many square metres, and therefore how many large tiles, are needed to cover the floor?
13. Cube container: A cube-shaped container has an edge length of 0.9 m. Find its volume in cubic metres.
14. Challenge: Find values of x, y, and z so that each of the expressions x², y³, and z⁶ has a value of 64.

Answers