Exponent

Definition

An exponent describes repeated multiplication.

Example:

2^3

means:

2 * 2 * 2 = 8

Exponent = compact notation for repeated multiplication.

---

Base And Exponent

In:

2^3

the base is:

2

the exponent is:

3

The exponent tells how many times the base is used as a factor.

Base is what gets multiplied; exponent tells how many factors.

---

Simple Examples

Examples:

3^2 = 3 * 3 = 9
4^3 = 4 * 4 * 4 = 64
10^2 = 10 * 10 = 100

Exponents make repeated multiplication easier to write.

Exponents compress repeated multiplication into a smaller expression.

---

Exponent Of One

Any value raised to exponent 1 stays itself.

Example:

5^1 = 5
x^1 = x

The base appears once.

Exponent 1 means one copy of the base.

---

Exponent Of Zero

For any nonzero base:

x^0 = 1

Example:

5^0 = 1

This rule keeps exponent patterns consistent.

Any nonzero base to the power of zero equals 1.

---

Why Exponents Matter

Exponents describe growth patterns.

Example:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

Each step multiplies by the same base.

Exponents represent repeated scaling.

---

Final Summary

• An exponent represents repeated multiplication.
• The base is the value being multiplied.
• The exponent tells how many factors are used.
• x^1 = x.
• For nonzero x, x^0 = 1.
• Exponents describe repeated scaling and growth.