Exponents in Math Explained | Grade 7 Questions, Examples, and Step-by-Step Solutions

Exponents are a fundamental concept in mathematics that show how many times a number, called the base, is multiplied by itself. On this page, you will find Grade 7 math examples and algebra questions involving exponents, along with clear, step-by-step solutions. These practice problems cover topics such as writing expressions with powers, evaluating exponents, and simplifying using exponent rules. Detailed solutions and explanations are included to help students, teachers, and parents build a strong understanding of exponents.

What are an exponents in maths and where are they used?

Exponents are a way to represent repeated multiplication of a number by itself. \[ \Large{\color{red}\underbrace{a \times a \times a \times \cdots \times a}_{n \ \text{times}} = a^n} \]

Example 1: Basic Exponentiation

\[ 5 \times 5 \times 5 = 5^3 \] Here:

Base = \(5\)
Exponent = \(3\)
Meaning: multiply 5 by itself 3 times.

Example 2: Representing Large Numbers

\[ 100{,}000 = 10 \times 10 \times 10 \times 10 \times 10 = 10^5 \]

Example 3: Representing Small Numbers

\[ 0.00001 = \frac{1}{100{,}000} = \frac{1}{10^5} = 10^{-5} \] A negative exponent means taking the reciprocal.

For example: \[ \large{\color{red}{10^{-2} = \frac{1}{10^2}} = \color{black}{\frac{1}{100}}} \]

Example 4: Units of Area

The area of a square of side \(1\) meter is: \[ 1 \,\text{m} \times 1 \,\text{m} = 1 \,\text{m}^2 \] Read as: 1 square meter.

Example 5: Units of Volume

The volume of a cube of side \(1\) meter is: \[ 1 \,\text{m} \times 1 \,\text{m} \times 1 \,\text{m} = 1 \,\text{m}^3 \] Read as: 1 cubic meter.

Example 6: Scientific Prefixes

Kilo: \(1000 = 10^3\)
Example: \[ 1 \,\text{kilogram} = 10^3 \,\text{grams} = 1000 \,\text{grams} \]
Mega: \(1{,}000{,}000 = 10^6\)
Example: \[ 1 \,\text{megabyte} = 10^6 \,\text{bytes} = 1{,}000{,}000 \,\text{bytes} \]
Giga: \(1{,}000{,}000{,}000 = 10^9\)
Example: \[ 1 \,\text{gigabyte} = 10^9 \,\text{bytes} = 1{,}000{,}000{,}000 \,\text{bytes} \]

Solve the following exponents problems.(Solutions and explanations included)

Exponent Practice Problems

Write the following using exponents:
1. \( 8 \times 8 \times 8 \times 8 \)
2. \( 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \)
3. \( A \times A \times A \)
4. \( \text{meter} \times \text{meter} \)
5. \( \text{centimeter} \times \text{centimeter} \times \text{centimeter} \)
Evaluate the following:
1. \( 2^4 \)
2. \( 10^4 \)
3. \( (-2)^4 \)
4. \( -2^4 \)
Use exponents to write the following using one power only:
1. \( 4 \times 8 \)
2. \( 25 \times 5 \)
3. \( 16 \times 4 \times 4^3 \)
4. \( 2 \times 2 \times 8 \times 2^3 \)
5. \( B \times B \times B^3 \)
Use exponents to rewrite the following expressions in simplified form:
1. \( 2^3 \times 2^4 \)
2. \( 6 \times 6^3 \)
3. \( 5 \times 5^2 \times 5^3 \)

Detailed Solutions and explanations are included.