This document discusses powers and exponents, including the order of operations when evaluating expressions with exponents. It provides examples of evaluating expressions where variables are replaced with given values, showing the step-by-step work. The examples demonstrate how to apply the rules of exponents and order of operations to simplify expressions containing powers and variables.

1. 4-2 Powers and Exponents
Objective: Use powers and exponents
in expressions and equations.

2. 5-Minute Quiz
Using the divisibility rules, state whether each number is
divisible by 2, 3, 5, 6, or 10.
1. 48
2. 155
3. 543
4. 1230
5. 345,678

3. 5-Minute Quiz
Using the divisibility rules, state whether each number is
divisible by 2, 3, 5, 6, or 10.
1. 48 2, 3, 6
2. 155 5
3. 543 3
4. 1230 2, 3, 5, 6, 10
5. 345,678 2, 3, 6

4. 4-2 Powers and Exponents
Order of Operations
1. Do all operations within grouping symbols; start
with the innermost grouping symbols.
2. Evaluate all powers from left to right.
3. Do all multiplication and division from left to
right.
4. Do all addition and subtraction from left to right.

5. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
a. –4x + z4

6. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
a. –4x + z4
–4x + z4 = -4(3) + (-2) 4 Replace x with 3 and z with –2.

7. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
a. –4x + z4
–4x + z4 = -4(3) + (-2) 4 Replace x with 3 and z with –2.
= -4(3) + 16 Evaluate the power.

8. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
a. –4x + z4
–4x + z4 = -4(3) + (-2) 4 Replace x with 3 and z with –2.
= -4(3) + 16 Evaluate the power.
= -12 + 16 Find the product of 4 and –3.

9. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
a. –4x + z4
–4x + z4 = -4(3) + (-2) 4 Replace x with 3 and z with –2.
= -4(3) + 16 Evaluate the power.
= -12 + 16 Find the product of 4 and –3.
=4 Find the sum.

10. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]

11. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]
2[(xy)2 – z3] = 2[(3*2)2 – (-2)3] Replace x with 3, y with 2,
and z with –2.

12. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]
2[(xy)2 – z3] = 2[(3*2)2 – (-2)3] Replace x with 3, y with 2,
and z with –2.
= 2[(6)2 – (-2)3] Evaluate the innermost
grouping symbols.

13. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]
2[(xy)2 – z3] = 2[(3*2)2 – (-2)3] Replace x with 3, y with 2,
and z with –2.
= 2[(6)2 – (-2)3] Evaluate the innermost
grouping symbols.
= 2[36 – (-8)] Evaluate the powers.

14. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]
2[(xy)2 – z3] = 2[(3*2)2 – (-2)3] Replace x with 3, y with 2,
and z with –2.
= 2[(6)2 – (-2)3] Evaluate the innermost
grouping symbols.
= 2[36 – (-8)] Evaluate the powers.
= 2[44] Do operations inside
grouping symbols.

15. 4-2 Powers and Exponents
Example
Evaluate each expression if x = 3, y = 2, and z = -2.
b. 2[(xy)2 – z3]
2[(xy)2 – z3] = 2[(3*2)2 – (-2)3] Replace x with 3, y with 2,
and z with –2.
= 2[(6)2 – (-2)3] Evaluate the innermost
grouping symbols.
= 2[36 – (-8)] Evaluate the powers.
= 2[44] Do operations inside
grouping symbols.
= 88 Find the product.

16. 4-2 Powers and Exponents

17. 4-2 Powers and Exponents

18. 4-2 Powers and Exponents

19. 4-2 Powers and Exponents
Assignment: 16 – 44 Even, 45 – 57 All (Page 178+)