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Mastering Exponent Properties: Multiply and Simplify

Explore multiplication properties of exponents, simplify expressions, practice scientific notation, & raise powers to powers. Complete warm-ups and quizzes for a solid understanding.

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Mastering Exponent Properties: Multiply and Simplify

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  1. Good Day • Have homework out to be checked!! • Put questions on the board!! • Complete the day 3 warm-up • Warm-up Quiz on Friday!!

  2. Essential Question:How can the rules for multiplying and dividing monomials be determined using other properties? 7–3 & 7-4 Multiplication Properties of Exponents

  3. Multiplying Powers You can write a power as a product of powers with the same base. Think of the power as the product of two factors. 86 = 8 x 8 x 8 x 8 x 8 x 8 86 = 8 x 8 x 8 x8 x 8 x 8 84x 82 83x 83 Notice the pattern in the exponents!! The sums 4 + 2 and 3 + 3 both equal 6, the exponent of 8.

  4. Property:Multiplying Powers with the Same Base For every nonzero number a and integers m and n, amx an = am+n Examples:

  5. Multiplying Powers in an Algebraic Expression Simplify each expression.

  6. More Practice

  7. Good Day!! • Have homework out to be checked • Put questions on the board • Complete the day 4 warm-up • Get your thinking caps on!!

  8. Put on your thinking caps!! • Simplify each expression. • 2x(3y) = • 3x3(2y2) = • 4x3(2y2)(2z) = • -2y2(3y2z)(4z3) =

  9. Multiplying Numbers inScientific Notation Simplify (7 x 102)(4 x 105). Write the answer in scientific notation. Now try this one: (2.5 x 108)(6 x 103)

  10. Good Morning • Have homework out to be checked!! • Prepare for warm-up quiz (sharpen pencils BEFORE the bell rings) • No Talking – Eyes on your own paper (10 min.)

  11. Investigation!!! You can use what you learned in the last lesson to find a shortcut for simplifying expressions with powers. Complete each statement. 5.) Make a conjecture! What pattern do you see in your answers? 6.) Use your pattern to simplify (86)3.

  12. Property: Raising a Power to a Power For every nonzero number a and whole numbers m and n, (am)n = amn Examples: Now you try it! 1.) Simplify (x3)6 2.) Simplify (a4)7 and (a-4)7

  13. Example 2 – Simplifying an expression with Powers Simplify Now try this one:

  14. Raising a Product to a Power You can use repeated multiplication to simplify expressions like (5y)3. Notice that (5y)3 = 53 y3 This is another property of exponents! Property: Raising a Product to a Power For every nonzero number a and b and whole number n, (ab)n = anbn. Example: (3x)4 = 34x4 = 81x4

  15. Example 3 – Simplifying a product raised to a power. Simplify Now try these:

  16. Example 4 – Simplifying a product raised to a power. Simplify Now try these:

  17. Tonight’s Assignment • Complete the 7-3 Homework assignment on your unit outline • Study for a quiz on 7-1 to 7-3

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