Exponentiation

Exponentiation is a mathematical operation that involves raising a number to a power. The number being raised to a power is called the base, and the power to which the base is raised is called the exponent.

Notation

The exponentiation operation is denoted using the caret symbol (^), with the base and exponent written on either side of the caret. For example, 2^3 represents 2 raised to the power of 3.

Example

Let's take the example of 2^3. This means we multiply 2 by itself 3 times: 2 * 2 * 2, which equals 8.

Properties of Exponentiation

1. Product of Powers: When multiplying two powers with the same base, you can add their exponents. For example, a^m * a^n = a^(m+n).
2. Power of a Power: When raising a power to another power, you can multiply the exponents. For example, (a^m)^n = a^(m*n).
3. Power of a Product: When raising a product to a power, you can distribute the power to each factor. For example, (ab)^n = a^n * b^n.

Study Guide

When studying exponentiation, it's important to understand the concept of the base and exponent, as well as the properties of exponentiation. Practice solving problems involving exponentiation to strengthen your understanding of the topic.

Key points to remember:

• Exponentiation involves raising a number to a power.
• The base is the number being raised to a power, and the exponent is the power to which the base is raised.
• Use the properties of exponentiation to simplify and solve expressions involving powers.

Don't forget to practice and review examples to solidify your understanding of exponentiation.