Grade 8 Integer Exponents Test – Free PDF

Contents

This grade 8 integer exponents test checks properties of integer exponents in 45 minutes, with 9 questions for a total of 20 points.

This test has 9 questions worth 20 points on the properties of integer exponents (8.EE.A.1). Calculators are not needed. Show the exponent steps for every question, and write final answers as fractions rather than decimals unless stated.

Test information

Grade: Grade 8
Chapter: Properties of Integer Exponents
Common Core: 8.EE.A.1
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 3 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 2 pts; Question 8: 2 pts; Question 9: 2 pts)

Grade 8 Integer Exponents Test: questions 1–5

Question 1: Evaluate powers (2 points)

Evaluate each expression.

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

Question 2: Positive exponent rules (3 points)

Write each expression as a single power.

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

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

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

Grade 8 Integer Exponents Test: questions 6–9

Question 6: Complete the table (2 points)

The table shows powers of 3.

Powers of 3.

Fill in the three missing values. (1 point)
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.

Cell counts.