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

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

3. 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 –

4. 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

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

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

7. 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

8. 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

9. 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.

10. 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

11. 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

12. – = = 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

13. 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

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

15. 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 –

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