Understanding Exponents Base Exponent 4 3 Power

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

How would you write this problem using exponents? 1. 2 • 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

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.

WATCH OUT! Any power raised to the zero power is automatically 1! 20 = 1 560 = 1 789,890,258,972,659,8720 = 1

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.

For example… 4-3 = 4 x 4 x 4 16 x 4 64 _1 _ 64

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

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

Can you solve these problems? 1. 4( 3 + 2)2 = 4(5)2 4(5•5) 4(25) =100 2. 2 • 52 + 4 • (-3)= -62 2x3 + 4y (x = -2 ; y = 3) 192 4. 3(a)2 + 6 ( a = 5) 81 -a4 (a = 2) -16 6. (-a)4 (a = 2) 16

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 = 343+32= 375

Remember the imaginary exponent 44+0 = 44 Right?? WRONG! 44 x 41 44+1 = 45 = 4x4x4x4x4 = 1,024