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Understanding the Multiplication of Exponents: Key Concepts and Common Mistakes

This comprehensive guide by Terri LeGault explores the multiplication of exponents, detailing the multiplication property which states that when multiplying two terms with the same base, you can add the exponents (x^m * x^n = x^(m+n)). It outlines essential examples, clarifies common mistakes (like mixing bases and exponents), and emphasizes the importance of applying the multiplication rule strictly to expressions with the same base. Additionally, worksheets and answers are included to reinforce learning.

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Understanding the Multiplication of Exponents: Key Concepts and Common Mistakes

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  1. Multiplication of Exponents By: Terri LeGault

  2. Multiplication of Exponents • Mulitplication Property: Whenever you multiply two terms with the same base you can add the exponents. xm * xn =x (m+n) , x raised to m times x raised to n equals x raised to m plus n. • Example: x5 *x2 =x (5+2) = (x*x*x*x*x)+(x*x)= (x*x*x*x*x*x*x)

  3. Multiplication Cont. • When you see this (xn)m, do not add m and n together, you multiply them. • Examples: (x2)5 = x10, 5 times 2. (73)4 = 712, 4 times 3. (21)-5 = 2-5, 1 times -5

  4. Common Mistakes • Do not multiply the base and the exponent. 3 to the power of 3 does not equal 9, it equals 27. • The Multiplication rule only applies to expressions with the same base.

  5. Mistakes Cont. • The multiplication rule applies just to the product, not to the sum of two numbers.

  6. Worksheet and Answers • Multiplication Property Worksheet • Answers for Worksheets

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