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Learn how to simplify expressions with integer exponents, apply exponent rules, and perform operations with exponents. Understand the concept of repeated multiplication and use exponential notation. Explore combining and dividing exponents. Master the distributive rule for exponents.
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Working with Powers • Integer Exponents • Exponent Rules • Order of Operations
Examples • 2 × 2 = • 2 × 2 × 2 = • 2 × 2 × 2 × 2 = • How can we write these in shorter notation?
3 × 3 × 3 × 3 × 3 = Examples • Multiplication is a shortcut for repeated addition. • Exponents are a shortcut for repeated multiplication. 3 + 3 + 3 + 3 + 3 = 5 × 3
Write these numbers using exponential notation: • 10,000 = 10? • 27 = 3? • 32 = 2?
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.
For Example 1 kilobyte (1K) = 210 = 1 megabyte (1 MB) = 220 =
Integer Exponents • Base 4 • Exponent 3 • 43 is called a power • 43 = 4 x 4 x 4 • = 64
You try these . . . • 72 • 54 • 210
Operations with Exponents • Multiply (x3)∙(x4) = (x ∙ x ∙ x) ∙ (x ∙ x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x ∙ x ∙ x ∙ x) = x7 A5∙ A4 = • Divide:
Exponent Rules #1 n times
Zero as an exponent • 40 • 90 • 170
a0 = 1 • M0 • (pq)0 • (2x2y)0
3-1 7-1 5-2 2-4 (1/2) -1 (3/4) -2 Negative Exponents
M-2 • x-5 • (1/y)-3
Combining Exponents aman=?
y-2y7 m6m-6 2z-3z5w-6w-2 • x5x4 • b3b-6 • (2x3)(4x-2)
Combining Exponents am/an=?
Combining Exponents (am)n=?
(w4)5 • (p-3)4 • (5x4)-2 • (-3y-7)3
Exponent Rules #7 (distributive rule for exponents)
Exponent Rules • 1. • 2. • 3.
4. 5. 6. 7. Exponent Rules