8th Grade Properties of Integer Exponents Test with Point Values (PDF)

8th Grade math test: Properties of Integer Exponents – Maths PDF

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This integer exponents test for 8th Grade covers properties of integer exponents (Common Core 8.EE.A.1), with a free PDF to print.

This 20-point test checks the properties of integer exponents, including zero and negative exponents (Common Core 8.EE.A.1). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Properties of Integer Exponents
Standards: 8.EE.A.1
Time: 45 minutes
Total: 20 points

Integer exponents test: questions

Question 1 – Use the rules [4 pts]

Simplify \(5^{2} \cdot 5^{4}\). (1 point)
Simplify \(\frac{7^{8}}{7^{5}}\) and evaluate. (1 point)
Simplify \(\left(3^{2}\right)^{3}\). (1 point)
Evaluate \(9^{0}\). (1 point)

Question 2 – Negative exponents [3 pts]

Each step to the right divides by 2, so the exponent drops by 1.

Write \(2^{-1}\) and \(2^{-2}\) as fractions. (2 points)
Evaluate \(10^{-2}\) as a decimal. (1 point)

Question 3 – Expand and count [2 pts]

5^2 × 5^3 = 5^5

Write the product shown as a single power and evaluate it.

Question 4 – Fractions [2 pts]

Evaluate \(\left(\frac{3}{4}\right)^{-2}\).

Question 5 – Multi-step [3 pts]

Simplify and write with positive exponents: \(\frac{3^{-2} \cdot 3^{7}}{3^{2}}\). Then evaluate.

Question 6 – Find the exponent [2 pts]

Find \(n\): \(\frac{4^{n}}{4^{3}} = 4^{-2}\).

Question 7 – Doubling [2 pts]

Followers double every week.

Mei’s video channel starts with 1 thousand followers, and the number doubles every week. Write the number of thousands after \(w\) weeks as a power. How many thousand followers are there after 8 weeks?

Question 8 – Explain [2 pts]

Liam says \(5^{-2} = -10\). Explain his mistake and give the correct value.

Key facts behind this integer exponents test

Key facts

Product rule: \(a^{m} \cdot a^{n} = a^{m+n}\).
Quotient rule: \(\frac{a^{m}}{a^{n}} = a^{m-n}\).
Power rule: \(\left(a^{m}\right)^{n} = a^{mn}\).
\(a^{0} = 1\) and \(a^{-n} = \frac{1}{a^{n}}\) for nonzero \(a\).
A negative exponent does not make the number negative: \(2^{-3} = \frac{1}{8}\).

How to use this integer exponents test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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