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Lesson 7-1 Multiplying Monomials

Lesson 7-1 Multiplying Monomials. p. 401. 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).

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Lesson 7-1 Multiplying Monomials

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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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