Learning Outcomes
- Recall the properties of exponents and use them to rewrite expressions containing exponents.
Review the following list of rules for simplifying expressions containing exponents, then try the problems listed below. If you need a refresher, return to the Algebra Essentials module for more explanation and demonstration.
The Product Rule of Exponents
For any real number [latex]a[/latex] and natural numbers [latex]m[/latex] and [latex]n[/latex], the product rule of exponents states that
The Quotient Rule of Exponents
For any real number [latex]a[/latex] and natural numbers [latex]m[/latex] and [latex]n[/latex], such that [latex]m>n[/latex], the quotient rule of exponents states that
The Power Rule of Exponents
For any real number [latex]a[/latex] and positive integers [latex]m[/latex] and [latex]n[/latex], the power rule of exponents states that
The Zero Exponent Rule of Exponents
For any nonzero real number [latex]a[/latex], the zero exponent rule of exponents states that
The Negative Rule of Exponents
For any nonzero real number [latex]a[/latex] and natural number [latex]n[/latex], the negative rule of exponents states that
The Power of a Product Rule of Exponents
For any real numbers [latex]a[/latex] and [latex]b[/latex] and any integer [latex]n[/latex], the power of a product rule of exponents states that
The Power of a Quotient Rule of Exponents
For any real numbers [latex]a[/latex] and [latex]b[/latex] and any integer [latex]n[/latex], the power of a quotient rule of exponents states that