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Powers & Exponents

Powers & Exponents. Section 8.1. What is a Perfect Square?. Perfect Square : A number multiplied by itself. 2•2 3•3 4•4 5•5 4, 9, 16, 25, 36, 47, 64, 81, 100, 121, 144…. What is Power?.

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Powers & Exponents

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  1. Powers & Exponents Section 8.1

  2. What is a Perfect Square? • Perfect Square: A number multiplied by itself. 2•2 3•3 4•4 5•5 4, 9, 16, 25, 36, 47, 64, 81, 100, 121, 144…

  3. What is Power? • Exponent – tells how many times the base is multiplied by itself. *This can be a number or a variable. • Base – the number or variable that is going to be raised to a power. • Power – The term for the expression

  4. Write each expression using exponents. 2•2•2•2•2 The base is 2 2 is multiplied 5 times. It is written: 2⁵ m•m•m•m The base is m m is multiplied 4 times. It is written: m⁴ 7 The base is 7 7 is multiplied 1 time. It is written: 7 ˈ

  5. Your Turn! 4•4•4•4•4•4•4 4⁷ x•x•x x³ 10 10ˈ

  6. Try this! (2)(2)(2)(-5)(-5) (2)³(-5)² or 2³(-5)² *You must use parenthesis for (-5)! (-1)(-1)(-1)(-1)(3)(3) (-1)⁴(3)² *You must use parenthesis for (-1)! 2•3•5•2•3•3 2²3³5*Put in numerical order by bases!

  7. Write each power as a multiplication espression 10² 10•10 b³ b•b•b x⁴y⁵ x•x•x•x•y•y•y•y•y 5a²b³ 5•a•a•b•b•b

  8. Your Turn! 2•2•2 2³ y•y•y•y y⁴ 5•a•a•b•b•a 5a³b² *Always list numbers first and then letters alphabetically!

  9. Order of Operations Review • PEMDAS • Parenthesis first! • Evaluate all powers (exponents) from left to right • Multiplication/Division from left to right • Addition/Subtraction from left to right 2•5³ means 2•5•5•5=250 (2•5)³ means (2•5)(2•5)(2•5)=1000

  10. Evaluate the Expression If m=2 evaluate the exp. 4m³ 4(2)³ = PEMDAS! 4(2•2•2) 4(8) 32 4m³ 4•m•m•m

  11. Evaluate the Expression 3x+y² if x = -2, & y = -3 3(-2)+(-3)² 3(-2)+(9) -6 + 9 3 -2(x³+1) -2[(x•x•x)+1] Now, x = -3 -2[(-3•-3•-3)+1] -2[(-27)+1] -2(-26) 52

  12. Your Turn Evaluate the Expression If m = 4, & n = 2 -5(m+n)² **Think PEMDAS -5(4+2) ² -5(6) ² -5(36) -180 Evaluate the Expression 3a³ if a = -2 3(-2) ³ 3(-2•-2•-2) 3(-8) -24

  13. Review Which is bigger? 5² 2⁵ 5•5=25 2•2•2•2•2 = 1024 Write each expression using exponents: 9•9•9•9 a•a•a•a•a 3 9⁴ a⁵ 3ˈ

  14. Review Cont… Write each power as a multiplication expression: 12⁴ x⁵ m⁴n³ 12•12•12•12 x•x•x•x•xm•m•m•m•n•n•n Evaluate the Expression if a = 3, b = -2, & c = 4 c³2a⁴ 3a²b 4•4•4 2(3)⁴ 3(3)²(-2) 64 2(81) 3(9)(-2) 162 -54

  15. Homework  Pg. 339/340 #14-40

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