### 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

### Try it

### Candela Citations

- Question ID 23844.
**Authored by**: Meacham,William, mb Sousa,James.**License**:*CC BY: Attribution*.**License Terms**: IMathAS Community License CC-BY + GPL - Question ID 52400.
**Authored by**: Jenck, Michael mb Lewis, Matthew.**License**:*CC BY: Attribution*.**License Terms**: IMathAS Community License CC-BY + GPL - Question ID 14054.
**Authored by**: Sousa, James.**License**:*CC BY: Attribution*.**License Terms**: IMathAS Community License CC-BY + GPL - Question ID 52398.
**Authored by**: Wicks, Edward.**License**:*CC BY: Attribution*.**License Terms**: IMathAS Community License CC-BY + GPL - Revision and Adaptation.
**Provided by**: Lumen Learning.**License**:*CC BY: Attribution*