Integer Exponents Test Answer Key with Scoring – Grade 8

Question 1 Evaluate powers (3 points)

1. Zero exponent: 1.
2. 3⁻⁴ = 181.
3. Five negative factors: −32.

(a) 1 (b) 181 (c) −32

Scoring: 1 point per part.

Question 2 One power (3 points)

1. 6 + (−2) = 4: 7⁴.
2. 4 − 9 = −5: 11⁻⁵.
3. (−2)(3) = −6: 5⁻⁶.

(a) 7⁴ (b) 11⁻⁵ (c) 5⁻⁶

Scoring: 1 point per part.

Question 3 Positive exponents (2 points)

Cube each factor: 2³ = 8 and (a⁻²)³ = a⁻⁶. So 8a⁻⁶ = 8a⁶.

8a⁶

Scoring: 1 point for 8a⁻⁶, 1 point for the positive exponent form.

Question 4 Table of powers of 4 (3 points)

Dividing by 4 at each step: 16 ÷ 4 = 4, 4 ÷ 4 = 1, 1 ÷ 4 = 14. Check the last box: 4⁻² = 116.

4, 1 and 14

Scoring: 1 point per value.

Question 5 Several rules at once (3 points)

Multiply: −5 + 8 = 3, so 2³. Divide: 3 − (−2) = 5, so 2⁵ = 32.

32

Scoring: 1 point for 2³, 1 point for 2⁵, 1 point for 32.

Question 6 Dev’s work (2 points)

Dev added the exponents, but a power of a power needs multiplication: 2 · 4 = 8. So (3²)⁴ = 3⁸ = 6,561.

3⁸ = 6,561

Scoring: 1 point for naming the error, 1 point for the correct power.

Question 7 Views multiply (2 points)

10⁷ ÷ 10³ = 10⁴ = 10,000.

10⁴ = 10,000 times as many

Scoring: 1 point for subtracting exponents, 1 point for 10,000.

Question 8 Reading a picture (2 points)

Three boxes of 2² is (2²)³. Multiply exponents: 2 · 3 = 6, giving 2⁶ = 64.

(2²)³ = 2⁶ = 64

Scoring: 1 point for the power of a power, 1 point for 64.