Raising to a Power Study Guide

What is Raising to a Power?

Raising a number to a power means multiplying the number by itself a certain number of times. The number being multiplied is called the base, and the number of times it is multiplied by itself is called the exponent.

Notation

Raising a number a to the power of n can be denoted as aⁿ, where a is the base and n is the exponent.

Example

If we have a³, this means we are multiplying a by itself 3 times: a * a * a.

Properties

When raising a number to a power, there are several properties to keep in mind:

• Product of Powers: When multiplying two powers with the same base, you can add the exponents: a^m * aⁿ = a^m+n
• Power of a Power: When raising a power to another exponent, you can multiply the exponents: (a^m)ⁿ = a^{m * n}
• Power of a Product: When raising a product to a power, you can distribute the power to each term: (ab)ⁿ = aⁿ * bⁿ

Practice Problems

Now, let's try some practice problems to reinforce the concept:

1. Calculate 2⁴
2. Simplify 3² * 3⁵
3. Determine (4³)²

Conclusion

Raising a number to a power is an important concept in mathematics, and understanding its properties and applications can be very helpful in various mathematical calculations and problem-solving scenarios.