Properties of Exponents (Powers)
1. Introduction
Power is an expression of this type
that represents the result of multiplying the base, a, by itself as many times as the exponent, b, indicates. We read it as "a to the power of b". Example 1: The base is 2 and the exponent is 3.
2. Exponents properties
Power of a product
Product of powers (same base)
Quotient of powers (same base)
Power of a quotient
Power of a power
Negative exponent
3. Examples
Example 2:
We have the multiplication of powers in the numerator, but we can't resolve it because there are different bases (2 and 3). In the denominator we have a power with a base of 6 (3·2).
By writing the power in the denominator as the multiplication of powers of bases 3 and 2, we then have the same bases in the numerator and denominator and can now apply the rules.
Example 3:
The difficulty in this problem is the parameters, or what is the same, the letters. We work with them the same way as we do with numbers (the parameters represent numbers after all).
We have the multiplication of powers in the numerator, but we can't resolve it because there are different bases (2 and 3). In the denominator we have a power with a base of 6 (3·2).
By writing the power in the denominator as the multiplication of powers of bases 3 and 2, we then have the same bases in the numerator and denominator and can now apply the rules.
Example 3:
The difficulty in this problem is the parameters, or what is the same, the letters. We work with them the same way as we do with numbers (the parameters represent numbers after all).