Neft Teacher · Learn It

Unit 6 · Standard 6.AT.5

Explore Numerical Expressions with Exponents

Lesson 6-3 · Learn It — how the math works

Why we're learning this

You're a sound engineer at a music studio. Each time you flip a switch, the volume doubles. The starting volume is 1 unit. After flipping the switch 3 times, the volume is 2³ = 2 × 2 × 2 = 8 units — that's 8 times louder! How loud does it get after more flips?

✱ Math Workbench

Learn It

What does an exponent mean?

An exponent is a small raised number that tells you how many times to multiply a number by itself. We say 2³ as "two to the third power."

Picture itSee what the math looks like before you read about it

Each figure is built from square groups of tiles, and the groups grow larger from one figure to the next.
Where you see this in real lifeEach figure is built from square groups of tiles, and the groups grow larger from one figure to the next.

Watch me solve itI do — read one step at a time

The problem looks like this
Tape diagram: 2 × 2 = 4, then 4 × 2 = 8, so 2³ = 8.2242 × 22284 × 244
  1. I want to find the value of 2³.
  2. The small 3 tells me to multiply 2 by itself 3 times.
  3. So I write 2 × 2 × 2.2 × 2 × 2
  4. First 2 × 2 = 4. Then 4 × 2 = 8.2 × 2 = 4
  5. So 2³ = 8.

Watch out — mistakes students make here

  • Did you multiply base by exponent (3 × 4)? The exponent counts factors.
  • The power is 3⁴, not 34. Write 3 × 3 × 3 × 3.
  • Did you add 4 + 3 = 7? The exponent tells you to multiply 4 by itself 3 times: 4 × 4 × 4.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now let's find 5². How many times do we multiply 5 by itself?
  2. The is 2, so we write 5 × 5.5 × 5
  3. What is 5 × 5?5 × 5
    Check this step
    Yes, 25. So 5² = 25.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table, write each as and find its value.
  • Start with 2⁴ = 2 × 2 × 2 × 2.

Solve: each exponential expression. Show the and the final value.

PowerRepeated MultiplicationValue
4³4 × 4 × 4
2⁶2 × 2 × 2 × 2 × 2 × 2
5³5 × 5 × 5
10⁴10 × 10 × 10 × 10

Stuck? Open one hint at a time.

Hint 1

Each row shows the repeated multiplication for you. Your job is to multiply the factors carefully.

Hint 2

Multiply left to right, keeping a running total. For 10⁴, watch the zeros pile up.

Hint 3

Row 1: 4 × 4 = 16, then 16 × 4 gives the value. Use the same running-total idea for the other rows.

Check my answer
✅ Answers:
  • 4³ → Value: 64
  • 2⁶ → Value: 64
  • 5³ → Value: 125
  • 10⁴ → Value: 10000
Multiply the listed factors with a running total: 4³ = 4 × 4 × 4 = 64, 2⁶ = 64 as well after six doublings, 5³ = 125, and 10⁴ = 10,000. Notice that 4³ and 2⁶ have the same value even though the bases and exponents differ, and that 10⁴ gains one zero for each factor of 10.

Turn & TalkSay it out loud with a partner

In the sound studio, the volume doubles each time you flip the switch. Why is the volume after 3 flips 2³ = 8 and not 2 × 3 = 6?

Try starting with:

  • After 3 flips the volume is ___ because we multiply 2 three times.Después de 3 cambios el volumen es ___ porque multiplicamos 2 tres veces.
  • It is not 6 because doubling means we ___, not add.No es 6 porque duplicar significa que ___, no sumar.
Use these wordsExponentBasePowerEvaluate