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5.2 More Work with Exponents and Scientific Notation

The Power Rule and Power of a Product or Quotient Rule for Exponents If a and b are real numbers and m and n are integers, then The Power Rule (ab) n = a n · b n Power Rule(a m ) n = a mn Power of a Product Power of a Quotient

Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 3·3 = x 4·2 Example = 5 3 · (x 2 ) 3 · y 3 = 125x 6 y 3 (5x 2 y) 3

If m and n are integers and a and b are real numbers, then: Product rule for exponents a m · a n = a m+n Power rule for exponents (a m ) n = a mn Power of a product (ab) n = a n · b n Power of a quotient Quotient rule for exponents Zero exponent a 0 = 1, a ≠ 0 Negative exponent Summary of Exponent Rules

Simplify each of the following expressions. Example

Simplify by writing the following expression with positive exponents. Example

Operations with Scientific Notation Multiplying and dividing with numbers written in scientific notation involves using properties of exponents.

Example Perform the following operations. = (7.3 · 8.1) (10 -2 · 10 5 ) = = 59,130 ( )( ) a. b.