Columbus State Community College Chapter 4 Section 6 Exponents, Order of Operations, and Complex Fractions

Exponents, Order of Operations, and Complex Fractions Simplify fractions with exponents. Use the order of operations with fractions. Simplify complex fractions.

Simplifying Fractions with Exponents EXAMPLE 1 Simplifying Fractions with Exponents Simplify. (a) 2 3 – The base is and the exponent is 3. 2 3 – 2 3 – = 3 factors of 2 3 – 4 9 2 3 – 8 27 –

Simplifying Fractions with Exponents EXAMPLE 1 Simplifying Fractions with Exponents Simplify. (b) 2 9 3 4 = 1 48 = 2 9 3 4 1 1 1 1 1 = 2 • 2 • 3 • 3 • 3 3 • 3 • 3 • 3 • 2 • 2 • 2 • 2 • 2 • 2 1 1 1 1 1

^ = ( ) Using Your Calculator Try these problems using your calculator. (a) 2 3 – TI 30X IIS ( c A b ) ^ (-) 2 3 3 = 8 27 –

= ( ) Using Your Calculator Try these problems using your calculator. 2 3 – TI 30 Xa ( c A b + – ) x y 2 3 3 = 8 27 –

x ^ ^ = ( ) ( ) Using Your Calculator Try these problems using your calculator. (b) 2 9 3 4 TI 30X IIS x ( c A b ) ^ 2 9 2 ( c A b ) ^ 3 4 3 = 1 48 Optional

x = ( ) ( ) Using Your Calculator Try these problems using your calculator. (b) 2 9 3 4 TI 30 Xa 4 81 ( c A b ) x y 2 9 2  27 64 ( c A b ) x y 3 4 3  x c A b c A b = 1 48 4 81 27 64

Order of Operations Order of Operations Step 1 Work inside parentheses or other grouping symbols. Step 2 Simplify expressions with exponents. Step 3 Do the remaining multiplications and divisions as they occur from left to right. Step 4 Do the remaining additions and subtractions as they occur from left to right.

Using the Order of Operations with Fractions EXAMPLE 2 Using the Order of Operations with Fractions Simplify. (a) 5 6 – 2 11 15 1 3 11 15 1 3 – = 11 15 – 5 = 6 15 2 5 5 6 – 2 2 5 = = 4 25 1 2 5 6 – 4 25 = 2 15 – 3 5

x – = ^ ( ) ( ) Using Your Calculator Use your calculator to simplify this expression. 5 6 – 2 11 15 1 3 TI 30X IIS x ( ) (-) c A b 5 6 ( Optional ) – ( c A b c A b ) 11 15 1 3 = 2 15 – ^ 2

– = = x = Using Your Calculator Use your calculator to simplify this expression. 5 6 – 2 11 15 1 3 TI 30 Xa – = c A b c A b 11 15 1 3 x y = 2 x = 2 15 – c A b + – 5 6

Using the Order of Operations with Fractions EXAMPLE 2 Using the Order of Operations with Fractions Simplify. 1 1 (b) 3 4 5 8 15 + 5 8 4 15 = 1 6 2 3 3 4 1 6 + 3 4 1 6 + 9 12 2 + = = 11 12 11 12

Complex Fractions Complex Fractions A complex fraction is a fraction in which the numerator and/or denominator contain one or more fractions.

Simplifying a Complex Fraction EXAMPLE 3 Simplifying a Complex Fraction Simplify: 4 9 – 1 3 4 9 – 1 3 1 4 9 – 1 3 = ÷ • 4 9 – 3 1 = 3 4 3 = – = 1 3 –

Exponents, Order of Operations, and Complex Fractions Chapter 4 Section 6 – Completed Written by John T. Wallace