Let's dive into two fundamental exponent rules: the Product of Powers and the Quotient of Powers. Understanding these rules will make simplifying expressions with exponents much easier. We'll define each rule, then compare them side-by-side.
The Product of Powers rule states that when multiplying two exponents with the same base, you add the exponents. Mathematically, it's represented as:
$a^m \cdot a^n = a^{m+n}$
Where 'a' is the base, and 'm' and 'n' are the exponents.
The Quotient of Powers rule states that when dividing two exponents with the same base, you subtract the exponents. Mathematically, it's represented as:
$\frac{a^m}{a^n} = a^{m-n}$
Where 'a' is the base, and 'm' and 'n' are the exponents.
| Feature | Product of Powers | Quotient of Powers |
|---|---|---|
| Rule | When multiplying powers with the same base, add the exponents. | When dividing powers with the same base, subtract the exponents. |
| Formula | $a^m \cdot a^n = a^{m+n}$ | $\frac{a^m}{a^n} = a^{m-n}$ |
| Operation | Multiplication | Division |
| Exponent Handling | Exponents are added. | Exponents are subtracted. |
| Example | $2^3 \cdot 2^2 = 2^{3+2} = 2^5 = 32$ | $\frac{3^5}{3^2} = 3^{5-2} = 3^3 = 27$ |
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! ๐