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Multiplying Exponents

Related Topics:
More Lessons for Arithmetic
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The following diagram shows the power rule for exponents. Scroll down the page for more examples and solutions on using the power rule for exponents.

Power Rule for Exponents

When a number in exponent notation is raised to a power we multiply the exponents.
Consider:

Text Box:   = (a × a) × (a × a) × (a × a)  =    = a6

This is known as the third law of exponents or power rule:

Text Box: (ax)y = axy

Example:

Simplify the following, giving your answers in exponent form

Text Box: a)  (52)3    b) (y6)2    c) (x3)4 × (x2)4    d) (a5)3 ÷ (a2)6

Solution:

Text Box: a)  (52)3 = 52×3 = 56     b) (y6)2 = y6×2 = y12     c) (x3)4 × (x2)4 = x3×4 × x2×4 = x12 × x8 = x12+8 = x20    d) (a5)3 ÷ (a2)6 = a5×3 ÷ a2×6 = a15 ÷ a12 = a15–12 = a3

Learn the Power Rule of Raising an Exponent to Another Exponent



Example of multiplying exponents
Simplify Exponential Expressions - Product and Power Rule
This video provides several examples of how to simplify exponential expressions. The product and power rule of exponents are emphasized.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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