Power

Power in mathematics refers to the number of times a number is multiplied by itself. It is denoted using the exponent notation.

Exponent Notation

The exponent notation is written as a superscript to the right of the base number. For example, in the expression 3⁴, 3 is the base and 4 is the exponent. This means 3 is multiplied by itself 4 times.

Calculating Powers

To calculate a power, multiply the base number by itself the number of times indicated by the exponent. For example, 2³ is equal to 2 * 2 * 2, which equals 8.

Properties of Powers

There are a few properties of powers that are important to understand:

1. Product of Powers: When multiplying powers with the same base, add the exponents. For example, a^m * aⁿ = a^m+n.
2. Quotient of Powers: When dividing powers with the same base, subtract the exponents. For example, a^m / aⁿ = a^m-n.
3. Power of a Power: When a power is raised to another power, multiply the exponents. For example, (a^m)ⁿ = a^m*n.
4. Zero Exponent: Any non-zero number raised to the power of 0 is equal to 1. For example, a⁰ = 1.
5. Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, a^-n = 1 / aⁿ.

Study Guide

Here are some key points to remember when studying powers:

• Understand the concept of a base and an exponent in a power expression.
• Practice calculating powers by multiplying the base by itself the number of times indicated by the exponent.
• Memorize the properties of powers and understand how to apply them in mathematical operations.
• Practice simplifying expressions involving powers using the properties of powers.

Remember to practice solving various problems involving powers to reinforce your understanding of the topic.

Good luck with your studies!

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