Fall Working with Powers Integer Exponents Exponent Rules Order of Operations

Fall Examples 2 × 2 = 2 × 2 × 2 = 2 × 2 × 2 × 2 = How can we write these in shorter notation?

Fall Examples Multiplication is a shortcut for repeated addition. Exponents are a shortcut for repeated multiplication = 5 × 3 3 × 3 × 3 × 3 × 3 =

Fall Write these numbers using exponential notation: 10,000 = 10 ? 27 = 3 ? 32 = 2 ?

Fall Computer Memory A byte is capable of storing one letter of the alphabet. For example, the word “math” requires four bytes to store in a computer. Bytes of computer memory are often manufactured in amounts equal to powers of 2.

Fall For Example 1 kilobyte (1K) = 2 10 = 1 megabyte (1 MB) = 2 20 =

Fall Integer Exponents Base 4 Exponent is called a power 4 3 = 4 x 4 x 4 = 64

Fall You try these

Fall Operations with Exponents Multiply (x 3 )∙(x 4 ) = (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x) = x 7 A 5 ∙ A 4 = Divide:

Fall Exponent Rules #1 n times

Fall Zero as an exponent

Fall Exponent Rules #2

Fall a 0 = 1 M 0 (pq) 0 (2x 2 y) 0

Fall Negative Exponents (1/2) -1 (3/4) -2

Fall Exponent Rules #3

Fall M -2 x -5 (1/y) -3

Fall Combining Exponents a m a n =?

Fall Exponent Rules #4

Fall y -2 y 7 m 6 m -6 2z -3 z 5 w -6 w -2 x 5 x 4 b 3 b -6 (2x 3 )(4x -2 )

Fall Combining Exponents a m /a n =?

Fall Exponent Rules #5

Fall

Fall Combining Exponents (a m ) n =?

Fall Exponent Rules #6

Fall (w 4 ) 5 (p -3 ) 4 (5x 4 ) -2 (-3y -7 ) 3

Fall Combining Exponents

Fall Exponent Rules #7 (distributive rule for exponents)

Fall

Fall Exponent Rules

Fall Exponent Rules