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

Question 1: Evaluate powers (2 points)

Evaluate each expression.

1. \(5^{3}\) (1 point)
2. \(10^{-3}\) (1 point)

Question 2: Positive exponent rules (3 points)

Write each expression as a single power.

1. \(6^{4}\cdot6^{7}\) (1 point)
2. \(\frac{9^{12}}{9^{5}}\) (1 point)
3. \((2^{5})^{3}\) (1 point)

Question 3: Negative exponent rules (3 points)

Write each expression as a single power. Then write the result without a negative exponent when the exponent is negative.

1. \(3^{-4}\cdot3^{9}\) (1 point)
2. \(\frac{7^{2}}{7^{6}}\) (1 point)
3. \((5^{-2})^{-3}\) (1 point)

Question 4: Show an equivalent expression (2 points)

Show that \(2^{6}\cdot2^{-9}\) is equivalent to \(\frac{1}{8}\).

Question 5: Zero and fraction bases (2 points)

Evaluate each expression.

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

Question 6: Complete the table (2 points)

The table shows powers of 3.

1. Fill in the three missing values. (1 point)
2. Write \(3^{-4}\) as a fraction. (1 point)

Question 7: Multi-step simplify (2 points)

Simplify \(\frac{(4^{3}\cdot4^{-5})^{2}}{4^{-2}}\) and write the answer as a fraction.

Question 8: Colony growth (2 points)

A colony has \(2^{5}\) cells. Each hour the count is multiplied by \(2^{3}\). Write the count after 1 hour and after 2 hours as single powers of 2, and give the count after 1 hour as a number.

Question 9: Find the error (2 points)

Aisha simplified \(\frac{5^{6}}{5^{2}}\) and wrote \(5^{3}\). Explain her error and give the correct result.

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