Assess Yourself

Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct—if you don't, review that part of the lesson.

$- 7$
$- 5$
$27$
$4$

Don't forget to raise 2 to the third power.

Follow the order of operations. Start by simplifying $1^{2}$ . $3 - 4 \cdot \left| 1.5 + 3.5 - 1^{2} \right| + \ 2^{3}$ $3 - 4 \cdot \left| 1.5 + 3.5 - 1 \right| + \ 2^{3}$ $3 - 4 \cdot \left| 5 - 1 \right| + \ 2^{3}$ $3 - 4 \cdot \left| 4 \right| + \ 2^{3}$ $3 - 4 \cdot \left| 4 \right| + \ 8$ $3 - 16 + 8$ $- 13 + 8$ $- 5$

The absolute value of $1.5 + 3.5 - 1^{2}$ is 4.

You need to fully simplify the expression within the absolute value signs and then multiply it by 4.

$(4 - 6)$
$2^{2}$
$\frac{1}{2} \div 4$
$2^{2} \cdot 3$

Look for the innermost operation and then work your way out, following the order of operations.

Start with the innermost set of grouping symbols.

You need to simplify within the innermost set of grouping symbols first.

${0.65}^{4}$
$0.65 \cdot 4$
$4^{0.65}$
$0.65 + 0.65 + 0.65 + 0.65$

Numbers written in exponential notation have the form $\textsf{base}^{\textsf{exponent}}$ .

This is another way to express the addition of $0.65 + 0.65 + 0.65 + 0.65$ .

For this problem the base is $0.65$ .

Addition is not the same operation as multiplication.

$- 198$
$9$
$142$
$- 18$

Simplify within the parentheses before moving on to other operations

Simplify within the parentheses before moving on to other operations.

Remember to simplify $5^{2}$ .

Follow the order of operations. Start by simplifying $5^{2}$ . $4^{2} - 8 \cdot \left( 5^{2} - 20 \right) + 6$ $4^{2} - 8 \cdot \left( 25 - 20 \right) + 6$ $4^{2} - 8 \cdot \left( 5 \right) + 6$ $16 - 8 \cdot \left( 5 \right) + 6$ $16 - 40 + 6$ $- 24 + 6$ $- 18$

Questions answered correctly:

Questions answered incorrectly:

How well do you understand the concepts and skills introduced in this lesson?

Let's Practice

1. Simplify $3 - 4 \cdot \left| 1.5 + 3.5 - 1^{2} \right| + 2^{3}$

2. To simplify $\left\lbrack \frac{1}{2} \div \left( 4 - 6 \right) + 2^{2} \right\rbrack \cdot \left( - 3 \right),$ which operation should you complete first?

3. Write the multiplication problem $0.65 \cdot 0.65 \cdot 0.65 \cdot 0.65$ using exponential notation.

4. Simplify $4^{2} - 8 \cdot \left( 5^{2} - 20 \right) + 6$ .

Summary

How well do you understand the concepts and skills introduced in this lesson?

Let's Practice

1. Simplify 3−4⋅|1.5+3.5−12|+23 3 - 4 \cdot \left| 1.5 + 3.5 - 1^{2} \right| + 2^{3}

2. To simplify [12÷(4−6)+22]⋅(−3), \left\lbrack \frac{1}{2} \div \left( 4 - 6 \right) + 2^{2} \right\rbrack \cdot \left( - 3 \right), which operation should you complete first?

3. Write the multiplication problem 0.65⋅0.65⋅0.65⋅0.65 0.65 \cdot 0.65 \cdot 0.65 \cdot 0.65 using exponential notation.

4. Simplify 42−8⋅(52−20)+6 4^{2} - 8 \cdot \left( 5^{2} - 20 \right) + 6 .

Summary

1. Simplify $3 - 4 \cdot \left| 1.5 + 3.5 - 1^{2} \right| + 2^{3}$

2. To simplify $\left\lbrack \frac{1}{2} \div \left( 4 - 6 \right) + 2^{2} \right\rbrack \cdot \left( - 3 \right),$ which operation should you complete first?

3. Write the multiplication problem $0.65 \cdot 0.65 \cdot 0.65 \cdot 0.65$ using exponential notation.

4. Simplify $4^{2} - 8 \cdot \left( 5^{2} - 20 \right) + 6$ .