Properties of Integer Exponents: Grade 8 Math Test Answer Key – PDF Download

Question 1: Evaluate powers (2 points)

1. \(5^{3}=5\cdot5\cdot5=\)125
2. \(10^{-3}=\frac{1}{10^{3}}=\)\(\frac{1}{1000}\)

Scoring: 1 point per part.

Question 2: Positive exponent rules (3 points)

1. \(4+7=11\), so \(6^{11}\)
2. \(12-5=7\), so \(9^{7}\)
3. \(5\cdot3=15\), so \(2^{15}\)

Scoring: 1 point per part for the correct power.

Question 3: Negative exponent rules (3 points)

1. \(-4+9=5\), so \(3^{5}\)
2. \(2-6=-4\), so \(7^{-4}=\)\(\frac{1}{7^{4}}\)
3. \((-2)(-3)=6\), so \(5^{6}\)

Scoring: 1 point per part.

Question 4: Show an equivalent expression (2 points)

Add exponents: \(6+(-9)=-3\), so the product is \(2^{-3}\). Then \(2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}\). The expressions are equal.

Scoring: 1 point for adding the exponents correctly, 1 point for converting to the fraction.

Question 5: Zero and fraction bases (2 points)

1. \((-9)^{0}=\)1
2. \((\frac{1}{2})^{-3}=2^{3}=\)8

Scoring: 1 point per part.

Question 6: Complete the table (2 points)

1. The values are \(1\), \(\frac{1}{3}\) and \(\frac{1}{9}\).
2. \(3^{-4}=\frac{1}{3^{4}}=\)\(\frac{1}{81}\)

Scoring: (a) 1 point for all three values. (b) 1 point.

Question 7: Multi-step simplify (2 points)

Inside: \(3+(-5)=-2\), so \(4^{-2}\). Power: \((4^{-2})^{2}=4^{-4}\). Divide: \(-4-(-2)=-2\), so \(4^{-2}=\)\(\frac{1}{16}\).

Scoring: 1 point for simplifying the parentheses and power, 1 point for the quotient and the fraction.

Question 8: Colony growth (2 points)

After 1 hour: \(2^{5}\cdot2^{3}=\)\(2^{8}\), which is 256. After 2 hours: \(2^{8}\cdot2^{3}=\)\(2^{11}\).

Scoring: 1 point for 2 to the 8th with 256, 1 point for 2 to the 11th.

Question 9: Find the error (2 points)

She divided the exponents, but the quotient rule subtracts them: \(6-2=4\). The correct result is \(5^{4}=625\).

Scoring: 1 point for identifying the error, 1 point for the correct value.

⬇ Download the Grade 8 Properties of Integer Exponents test answer key (PDF, 97 KB)

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