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Understanding Monomials: Multiplication and Simplification Techniques

Learn what monomials are, how to multiply them, simplify expressions, and recognize general rules. Practice determining monomials, simplifying expressions, and applying power rules. Master the basics step by step in this comprehensive lesson.

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Understanding Monomials: Multiplication and Simplification Techniques

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  1. Lesson 7-1 Multiplying Monomials p. 401

  2. What is a monomial? • A Monomial is a number, a variable, or a product of numbers and variables. • Monomials are similar to terms • Terms that are divided by a variable are not monomials. • Constants – monomials without variables (only numbers)

  3. Determine whether each expression is a monomial. -5 x Yes No, contains addition Yes No, contains division of variables Yes, could be written as Examples

  4. Review Powers • Remember that means • Similarly means • So • And • Can you think of a general rule?

  5. Product of Powers • To multiply two powers that have the same base, add the exponents • For any number a and all integers m and n, Ex. Simplify • Multiply all numbers • Combine all like variables by adding exponents • Rewrite your answer

  6. Problems to Try Determine whether each expression is a monomial. Explain. 1. 2. 3. 4. Simplify 5. 6.

  7. More to think about Consider And Can you think of a general rule?

  8. Power of a Power • To find the power of a power, multiply the exponents • For any number a and all integers m and n, • Ex. Simplify

  9. One more… • Consider • And • Can you think of a general rule?

  10. Power of a Product • To find the power of a product, find the power of each factor and multiply. • For all numbers a and b and any integer m, Ex. Find the area of the square

  11. Problems to Try Simplify 1. 2. Find the volume of a cube with side length

  12. Simplifying Monomial Expressions • When a monomial is simplified: • There is only one of each variable • There are no powers of powers • All fractions are simplified Ex. Simplify (use order of operations)

  13. Problem to Try 1. Simplify

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