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Write and Evaluate Numerical Expressions Involving Whole-Number Exponents

Show your work for all evaluation problems. Write the expanded form (repeated multiplication) before computing the final value.

Grade 6·20 problems·~35 min·Common Core Math - Grade 6·standard·6-ee-a-1
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

What is 9 × 9?

2.

Which expression uses 6 as a factor?

3.

What is 2 × 2 × 2 × 2?

B

Fluency Practice

Diagram of the expression 4 squared with arrows labeling the base as 4 and the exponent as 2, plus a prompt asking what the exponent tells you
1.

In the expression 424^2, what does the exponent tell you?

2.

Evaluate 626^2.

3.

Evaluate 535^3. Show your work as repeated multiplication.

4.

Evaluate 343^4. Show your work as repeated multiplication.

5.

What is the value of 10310^3?

C

Varied Practice

1.

Write 7 × 7 × 7 × 7 in exponential form:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ^  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   , then evaluate:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

base:
exponent:
value:
2.

A square has a side length of 8 units. Which exponential expression represents its area?

3.

Evaluate 262^6. Show your work as repeated multiplication.

Table showing powers of 10 from 10 to the first through 10 to the third power with completed values, and a highlighted fourth row for 10 to the fourth power with blank value and zero-count cells
4.

A student says 104=4010^4 = 40 because 10×4=4010 \times 4 = 40. What is the correct value of 10410^4?

D

Word Problems

1.

A square floor tile measures 7 centimeters on each side.

Write an exponential expression for the tile's area:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ^  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Then evaluate it:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   square centimeters.

base:
exponent:
area:
2.

A storage cube has a side length of ss centimeters.

1.

If the side length is 2 cm, write an exponential expression for the cube's volume:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ^  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Then evaluate it:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cubic centimeters.

base:
exponent:
volume:
2.

If the side length is 3 cm, write an exponential expression for the cube's volume:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ^  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Then evaluate it:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cubic centimeters.

base:
exponent:
volume:
3.

If the side length is 5 cm, write an exponential expression for the cube's volume:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ^  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Then evaluate it:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cubic centimeters.

base:
exponent:
volume:
E

Error Analysis

Two-column prompt card showing Priya's incorrect work for 4 cubed on the left and prompts about the base, exponent, and number of factors on the right
1.

Priya evaluated 434^3:
43=4×3=124^3 = 4 \times 3 = 12

What mistake did Priya make?

Two-column prompt card showing Marcus's incorrect work for 2 to the fifth on the left and prompts about the base, exponent, and operation on the right
2.

Marcus evaluated 252^5:
25=2+2+2+2+2=102^5 = 2 + 2 + 2 + 2 + 2 = 10

What mistake did Marcus make?

F

Challenge / Extension

1.

Find a whole number nn such that 2n=642^n = 64. What is nn?

2.

Evaluate both 232^3 and 323^2. Are they equal? Explain in your own words why you cannot simply swap the base and the exponent and expect the same answer.

0 of 20 answered