1. 1
Introduction to Algebra:
Integers

2. R.1 Fractions
1.8 Exponents and Order of Operations
Objectives
Use exponents to write repeated factors.
Simplify expressions containing exponents.
Use the order of operations.
Simplify expressions with fraction bars.

3. Use exponents to write repeated factors.
An exponent can be used to represent repeated multiplication.
The base is the number being repeatedly multiplied.

4. Simplifying expressions containing exponents.
Simplify each expression.
(–5)2
(b) (–5)3
Example

5. Simplifying expressions containing exponents.
Simplify the expression.
Example

6. Use the order of operations.

7. Use the order of operations.
Simplify.
9 + 3(20 – 4) ÷ 8
Example
9 + 3(20 – 4) ÷ 8
Work inside parentheses first.
(16) ÷ 8
Work left to right performing multiplication and division.
÷ 8
Add last. 15

8. Use the order of operations.
Simplify.
3 + 2(6 – 8) • (15 ÷ 3)
Example
3 + 2(6 – 8) • (15 ÷ 3)
Work inside parentheses first.
3 + 2(–2) • (5)
Work left to right performing multiplications.
3 + –4 •
–20
Add last.
–17

9. Use the order of operations.
Simplify.
(–4)3 – (4 – 6)2(–3)
Example
(–4)3 – (4 – 6)2(–3)
Work inside parentheses first.
(–4)3 – (–2)2(–3)
Simplify exponents.
–64 – 4(–3)
Multiply.
–64 – (–12)
Change subtraction to addition and add –
–52

10. Use the order of operations.

11. Simplify expressions with fraction bars.
Example
Simplify the numerator.
Simplify the denominator.
–8 + 5(4 – 6)
4 – 42 ÷ 8
4 – 16 ÷ 8
– (–2)
4 –
–8 + (–10) 2
–18
Simplify the fraction.