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Understanding Exponents
Base Exponent 4 3 Power
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Exponential Form Expanded Form Standard Form
4 Exponential Form 3 1 3 3 3 Expanded Form 3 x 3 x 3 x 3 2 4 3 3 Multiply 3x3x3x3 = 81 Standard Form 81
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How would you write this problem using exponents?
• 2 • 2 • 2 • 2 • 2 • 2 = 27 2. (-3)(-3) (-3)(-3) = (-3)4 3. a • a • a • a • a • a • a • a = a8 4. a • m • m • a • m • a • a = a4 m3 5. p • 2 • r • r • r • p • 2 = 22 p2 r3
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Remember… An exponent does not just mean multiply by that number!
An exponent means multiply the base times itself as many times as the exponent says.
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WATCH OUT! Any power raised to the zero power is automatically 1!
20 = 1 560 = 1 789,890,258,972,659,8720 = 1
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Negative Exponents? A number with a negative exponent means to…
Solve the multiplication as normal Move the answer to the denominator of a fraction under a 1.
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For example… 4-3 = 4 x 4 x 4 16 x 4 64 _1 _ 64
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What if there isn’t an exponent?
There’s always an exponent! Even if there isn’t one printed, there is always an imaginary exponent of 1. EX: 4 = 41
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What’s the difference? ( 5 + 5)2 vs. 52 (10) 2 5x5 10x10 25 100
PAY ATTENTION TO WHERE THE EXPONENT IS & FOLLOW THE ORDER OF OPERATIONS
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Can you solve these problems?
1. 4( 3 + 2)2 = 4(5)2 4(5•5) 4(25) =100 • • (-3)= -62 2x3 + 4y (x = -2 ; y = 3) 192 4. 3(a) ( a = 5) 81 -a4 (a = 2) -16 6. (-a)4 (a = 2) 16
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Multiplying Exponents
When the base is the same just add the exponents together If the bases are different you can’t combine them so solve as normal EX: 52 x 54 = 52+4 = 56 = 5x5x5x5x5x5 = 15,625 73 x 25 = 73 x 25 = 7x7x7x2x2x2x2x2 = = 375
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Remember the imaginary exponent
44+0 = Right?? WRONG! 44 x = 45 = 4x4x4x4x4 = 1,024
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