Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
ExponentSpanish: Exponente	A small number that tells how many times to multiply a number by itself.	In 9^4, the exponent is 4.
BaseSpanish: Base	The number that gets multiplied by itself.	In 9^4, the base is 9.
PowerSpanish: Potencia	A number written with a base and an exponent, like 2³.	9^4
EvaluateSpanish: Evaluar	To find the value by putting numbers in for the letters.	Evaluate 3⁴: write 3 × 3 × 3 × 3, then multiply step by step: 9 × 9 = 81
Repeated multiplicationSpanish: Multiplicación repetida	Multiplying the same factor again and again.	9 × 9 × 9 × 9
Expanded formSpanish: Forma desarrollada	A power written out as a product of its factors.	2^3 = 2 × 2 × 2

How it worksWorked examplewriting repeated multiplication as a power

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Write 9 × 9 × 9 × 9 as a power. Then name its base and its exponent.

Find the repeated factor. The factor is 9.
Count how many times it is used. It is used 4 times.
Write the base, then the exponent. 9 ^ 4
Read it out loud. 9 to the 4th power

Answer: 9 × 9 × 9 × 9 = 9^4. The base is 9 and the exponent is 4.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Write 6 × 6 × 6 as a power. Then name its base and its exponent.

Find the repeated factor. The factor is .
Count how many times it is used. times
Write the base, then the exponent. ^
Read it out loud. to the power

Answer:the power, its base, and its exponent

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

In this power, the base is and the exponent is .
The exponent tells me to use the base as a factor times.
I read this power as to the power.
A power shows repeated , not repeated .

Word bank powerbaseexponentfactorrepeated multiplicationexpanded formsquaredcubedevaluateproductreadtimes

Watch outA common mistake

A common mistake in Powers and Exponents is multiplying the base by the exponent instead of using the base as a repeated factor — for example, thinking 2³ = 2 × 3 = 6 instead of 2³ = 2 × 2 × 2 = 8. Before you submit, rewrite the power as repeated multiplication first, then multiply step by step.

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
Which expression shows 5³ as repeated multiplication?
1. A3 × 3 × 3 × 3 × 3
2. B5 × 5 × 5
3. C5 × 3
4. D5 + 5 + 5
Hint In 5³ the base is 5 and the exponent is 3. Ask: which number repeats, and how many times?
Show your work
2Complete the table. Show how you found each value.

Write each power as repeated multiplication, then find the value.

Power Repeated Multiplication Value
3² 3 × 3
2⁴ 2 × 2 × 2 × 2

Hint The middle column already shows each power as repeated multiplication — use it!
Show your work

Power	Repeated Multiplication	Value
3²	3 × 3
2⁴	2 × 2 × 2 × 2

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
What is the value of 4³?
1. A7
2. B12
3. C43
4. D64
Hint Look at the small raised 3. That exponent counts how many 4's get multiplied — it is not a number to multiply 4 by.
Show your work
4Circle the letter of the best answer. Show how you know.
What is the value of 6²?
1. A8
2. B12
3. C36
4. D62
Hint The little 2 is the exponent. It counts how many 6's you multiply — it's not a number to add or multiply by.
Show your work
5Circle the letter of the best answer. Show how you know.
Evaluate: 3 × (4 + 2)²
1. A36
2. B54
3. C108
4. D144
Hint There are three jobs here: parentheses, an exponent, and multiplication. Order of operations decides which comes first.
Rewrite the whole expression each line What I simplified
1. 1GroupingInside ( ) first.
2. 2ExponentsThen powers.
3. 3× ÷Left to right.
4. 4+ −Left to right.

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
1. 1Expression5³
2. 2Student's thinking5 × 3
3. 3Calculate= 15
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Does the exponent tell you to multiply the base BY the exponent, or to use the base as a factor that many times?
Correct work
Correct answer:

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

Sentence starter When the exponent increases by 1, the value is multiplied by ___ because the base is used as a factor ___ more time.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Evaluate each exponential expression. Show the repeated multiplication and the final value.

Power Repeated Multiplication Value
4³ 4 × 4 × 4
2⁶ 2 × 2 × 2 × 2 × 2 × 2
5³ 5 × 5 × 5
10⁴ 10 × 10 × 10 × 10

Show your work
2Write the name of the correct group on each line.
Sort each power by whether its value is greater than 50 or not.

Groups: Value > 50 Value ≤ 50
- 2⁵
- 3⁴
- 7²
- 10²
- 5³
- 4²
3Write the letter of the matching item on each line.
Match each power to its value.
1. 2⁵
2. 3³
3. 4³
4. 10³
5. 5²
6. 2⁷
- A32
- B27
- C64
- D1000
- E25
- F128
4Decide whether each pair balances. Check Yes or No, then explain.

Compare: 3⁴ vs. 4³

Left side Right side Balanced?

Explain your choice

Power	Repeated Multiplication	Value
4³	4 × 4 × 4
2⁶	2 × 2 × 2 × 2 × 2 × 2
5³	5 × 5 × 5
10⁴	10 × 10 × 10 × 10

Part 2Explain and correctreasoning

5Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
1. 1Expression2⁴
2. 2Student's thinking2 × 4
3. 3Calculate= 8
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Compare the values when the base and exponent are swapped. What do you notice?

Expression A Value A Expression B Value B Which is greater?
2⁵ 5²
2⁴ 4²
3⁴ 4³

Show your work

Part 2Explain and correctreasoning

2Find the mistake. Explain it, then show the correct work.
Find the Exponent Error
1. 1Expression2³
2. 2Student's thinking2 × 3
3. 3Calculate= 6
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
3Answer in complete sentences.

A bacteria colony doubles every hour. Starting with 1 bacterium, write a power expression for the number after 6 hours. Explain why exponential growth is so much faster than adding the same number each hour.
Write your answer

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Rewrite the whole expression each line	What I simplified

Expression A	Value A	Expression B	Value B	Which is greater?
2⁵		5²
2⁴		4²
3⁴		4³