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**Columbus State Community College**

Chapter 4 Section 6 Exponents, Order of Operations, and Complex Fractions

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**Exponents, Order of Operations, and Complex Fractions**

Simplify fractions with exponents. Use the order of operations with fractions. Simplify complex fractions.

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**Simplifying Fractions with Exponents**

EXAMPLE 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 –

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**Simplifying Fractions with Exponents**

EXAMPLE 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

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**^ = ( ) Using Your Calculator**

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

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**= ( ) Using Your Calculator Try these problems using your calculator.**

2 3 – TI 30 Xa ( c A b + – ) x y 2 3 3 = 8 27 –

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**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

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**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

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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.

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**Using the Order of Operations with Fractions**

EXAMPLE 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

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**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

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**– = = 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

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**Using the Order of Operations with Fractions**

EXAMPLE 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

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

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**Simplifying a Complex Fraction**

EXAMPLE 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 –

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**Exponents, Order of Operations, and Complex Fractions**

Chapter 4 Section 6 – Completed Written by John T. Wallace

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