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  Using the Laws of Exponents to Simplify Expressions

In this example about the laws of exponents, two exponents are added.

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Review of the laws of exponents:

This set of Math Tutorials addresses the topic of the laws of exponents. We look at the following types of expressions that utilize the laws of exponents:

x^a•x^b

x^a•x^b•x^c

x^a/x^b

x^a•x^b/x^c

In each expression the terms a, b, and c are integers. In all cases, x is the common base, and so the laws of exponents can be used:

• When there is a common base and two terms are being multiplied, add the exponents.
• Where there is a common base and two terms are being divided, subtract the exponent in the denominator from the exponent in the numerator.
• When there is a common base and there is a combination of multiplicaton and division, apply the laws of exponents to pairs of terms in going from left to right.

Using the laws of exponents requires that you be familiar with multiplying and dividing expressions expressed with exponents.

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Tweet Learn More About Math Tutorials

The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.

Our current inventory of Math Examples include:

• Math Tutorial: Examples Using Algebra Tiles
• Math Tutorial: Solving Equations in One Variable
• Math Tutorial: Solving Equations with Fractions
• Math Tutorial: Midpoint formula
• Math Tutorial: Distance formula
• Math Tutorial: Graphing linear functions, given m and b
• Math Tutorial: Graphing absolute value functions
• Math Tutorial: Graphing linear inequalities
• Math Tutorial: Solving quadratics by completing the square
• Math Tutorial: Factoring Quadratics
• Math Tutorial: Polynomial Expansion
• Math Tutorial: Solving quadratics using the quadratic formula
• Math Tutorial: Using FOIL
• Math Tutorial: Graphs of Exponential Functions
• Math Tutorial: Laws of Exponents