BASE OF A POWER

Definition Of Base (Of A Power)

In an expression of the form x^y, x is the base. The base x is a factor that repeats y times.

Examples of Base (of a Power)

In 3⁴, 3 is the base. The factor 3 would repeat 4 times, i.e. 3 × 3 × 3 × 3.
In 5², 5 is the base. The factor 5 would repeat twice, i.e. 5 × 5.

Video Examples: Basic Algebra

Solved Example on Base (of a Power)

Ques: Which is the base in 'six to the fourth power'?

Choices:

A. 6
B. 4
C. 2
D. 10
Correct Answer: A

Solution:

Step 1: 'Six to the fourth power' is 6⁴
Step 2: The base here is 6.

Quick Summary

The base is the number being multiplied by itself.
The exponent indicates how many times the base is multiplied.

\[ x^y \]

🍎 Teacher Insights

Use real-world examples like repeated addition to illustrate the concept of exponents and the base.

🎓 Prerequisites

Basic Arithmetic
Understanding of Factors

Check Your Knowledge

Q1: What is the base in 7^3?

A. 7 B. 3 C. 21 D. 343

Q2: In the expression 'five to the power of two', which number is the base?

A. 2 B. 5 C. 7 D. 10

Frequently Asked Questions

Q: What does 'base' mean in mathematics?
A: The base is the number being raised to a power. It's the number you're multiplying by itself a certain number of times.

Q: How do I identify the base in an exponential expression?
A: The base is the number that is written normally (not as a superscript) in an exponential expression.