Learning Outcomes
- Simplify expressions with exponents and integer bases
- Simplify expressions with exponents and rational bases
Remember that an exponent indicates repeated multiplication of the same quantity. For example, [latex]{2}^{4}[/latex] means to multiply four factors of [latex]2[/latex], so [latex]{2}^{4}[/latex] means [latex]2\cdot 2\cdot 2\cdot 2[/latex]. This format is known as exponential notation.
Exponential Notation
This is read [latex]a[/latex] to the [latex]{m}^{\mathrm{th}}[/latex] power.
In the expression [latex]{a}^{m}[/latex], the exponent tells us how many times we use the base [latex]a[/latex] as a factor.
Before we begin working with variable expressions containing exponents, let’s simplify a few expressions involving only numbers.
example
Simplify:
1. [latex]{5}^{3}[/latex]
2. [latex]{9}^{1}[/latex]
Solution
1. | |
[latex]{5}^{3}[/latex] | |
Multiply [latex]3[/latex] factors of [latex]5[/latex]. | [latex]5\cdot 5\cdot 5[/latex] |
Simplify. | [latex]125[/latex] |
2. | |
[latex]{9}^{1}[/latex] | |
Multiply [latex]1[/latex] factor of [latex]9[/latex]. | [latex]9[/latex] |
try it
example
Simplify:
1. [latex]{\left({\Large\frac{7}{8}}\right)}^{2}[/latex]
2. [latex]{\left(0.74\right)}^{2}[/latex]
try it
example
Simplify:
1. [latex]{\left(-3\right)}^{4}[/latex]
2. [latex]{-3}^{4}[/latex]