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

Lesson 6.36.3 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
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.

  1. Find the repeated factor. The factor is 9.
  2. Count how many times it is used. It is used 4 times.
  3. Write the base, then the exponent. 9 ^ 4
  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.

  1. Find the repeated factor. The factor is .
  2. Count how many times it is used. times
  3. Write the base, then the exponent. ^
  4. 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 6.36.3 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    PowerFactorsValue
    3⁴3 × 3 × 3 × 3?
    4³4 × 4 × 4?
    Same two numbers, switched places.

    Is 3⁴ greater than 4³? Find both values.

    1. 1Find the value of 3⁴.
    2. 2Find the value of 4³.
    3. 3Which is greater? By how much?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Divide by 5Result
    625 ÷ 5?
    ? ÷ 5?
    ? ÷ 5?
    ? ÷ 51
    Each division by 5 removes one factor of 5.

    Write 625 as a power of 5.

    1. 1Divide 625 by 5 again and again until you reach 1. List the results.
    2. 2How many times did you divide by 5? That is the exponent.
    3. 3Write 625 as a power.
    4. 4Why is 5⁴ not the same as 5 × 4?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the value of 0.3².

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Write 128 as a power of 2. What is the exponent?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    HoursCellsPower
    122¹
    242²
    382³
    The exponent matches the number of hours.

    One cell splits into 2 cells every hour. Each new cell splits too. You start with 1 cell. How many cells are there after 8 hours?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    How much greater is 2¹⁰ than 10²?

    Show your work
    Final answer:

Explain your thinkingDoes a bigger base always give a bigger power? Use 3⁴ and 4³ to explain your answer.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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