Full Prep Academy

Overview

An exponent represents repeated multiplication of the same number. It is written as a base raised to an exponent, for example, \( a^n \), where \( a \) is the base and \( n \) is the exponent. The exponent tells us how many times to multiply the base by itself.

Example

For \( 3^4 \), the base is \( 3 \), and the exponent is \( 4 \). This means:

\( 3^4 = 3 \times 3 \times 3 \times 3 = 81 \)

Key Concepts

• Base: The number that is being multiplied.
• Exponent: The number of times the base is multiplied by itself.

Example 1: Simplifying an Exponent

Consider the expression \( 2^3 \):

\( 2^3 = 2 \times 2 \times 2 = 8 \)

Example 2: Large Exponent

For \( 5^2 \):

\( 5^2 = 5 \times 5 = 25 \)

Practice Questions

1. Question 1: Simplify the following expression: \( 2^5 \)
   Solution

   Step 1: Multiply the base \( 2 \) five times:

   \( 2 \times 2 \times 2 \times 2 \times 2 = 32 \)

2. Question 2: Simplify the following expression: \( 4^3 \)
   Solution

   Step 1: Multiply the base \( 4 \) three times:

   \( 4 \times 4 \times 4 = 64 \)

3. Question 3: Simplify the following expression: \( 3^6 \)
   Solution

   Step 1: Multiply the base \( 3 \) six times:

   \( 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729 \)

4. Question 4: Simplify the following expression: \( 6^2 \)
   Solution

   Step 1: Multiply the base \( 6 \) two times:

   \( 6 \times 6 = 36 \)

5. Question 5: Simplify the following expression: \( 7^4 \)
   Solution

   Step 1: Multiply the base \( 7 \) four times:

   \( 7 \times 7 \times 7 \times 7 = 2401 \)