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Simplify each expression.

Warm Up #7. Simplify each expression. 1. ( – 2) 3. – 8. 2. 5 2 – 3 4. – 56. 3. A gigabyte is about 10 3 megabytes. A music player has 4 gigabytes of memory. About how many megabytes is this?. 4000 megabytes. 5.1 Use properties of Exponents.

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Simplify each expression.

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  1. Warm Up #7 Simplify each expression. 1. (–2)3 –8 2. 52 – 34 –56 3. A gigabyte is about 103 megabytes. A music player has 4 gigabytes of memory. About how many megabytes is this? 4000 megabytes

  2. 5.1 Use properties of Exponents Objective: Simplify expressions involving powers

  3. 7. (–4 25)2 = 16 252 = 16,384 = 16 210 = (– 4)2(25)2 –1 115 118 = 9. 118 115 = 1331 = 113 EXAMPLE 1 Evaluate numerical expressions Power of a product property Power of a power property Simplify and evaluate power. Negative exponent property = 118–5 Quotient of powers property Simplify and evaluate power.

  4. = (8.5 107)(1.2 103) = (8.5 1.2)(107 103) = 10.21010 = 1.02 1011010 = 1.02 1011 = 85,000,000 1200 EXAMPLE 2 Use scientific notation in real life A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 squarekilometers. About how many locusts are in such a swarm? Write in scientific notation. Use multiplication properties. Product of powers property Write 10.2 in scientific notation. Product of powers property

  5. 2 3 3. 9 for Examples 1 and 2 GUIDED PRACTICE Evaluate the expression. 1. (42 )3 4096 ANSWER 2.(–8)(–8)3 4096 ANSWER 8 ANSWER 729

  6. 6 10 – 4 9 107 18. for Examples 1 and 2 GUIDED PRACTICE

  7. = b–4 +6+7 = b9 s–2–3 (s–2 )–3 ( s3 )–3 = 10. s3 s 6 = s–9 11. 16m4n –5 2n–5 EXAMPLE 3 Simplify expressions Product of powers property 5. b–4b6b7 Power of a quotient property Power of a power property = s15 Negative exponent property Quotient of powers property = 8m4n –5 – (–5) = 8m4n0= 8m4 Zero exponent property

  8. 1 = x11 (x–3)2(y3)2 (x–3y3)2 = x5y6 x5y6 x –6y6 = x5y6 EXAMPLE 4 Standardized Test Practice #16 = x –6– 5y6– 6 = x–11y0

  9. for Examples 3, 4, and 5 GUIDED PRACTICE Simplify the expression. 6. x–6x5 x–3 4. (7y2z5)(y–4z–1) x–4 7y-2z4

  10. x4y–2 3 s 3 2 14. 15. t–4 x3y6 for Examples 3, 4, and 5 GUIDED PRACTICE

  11. Classwork/Homeworkpages 333-334 (3-39 multiples of 3, and #52)

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