Multiplying Exponents

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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:

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

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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.

Show Step-by-step Solutions

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