8th Grade Properties of Integer Exponents Test Solutions and Scoring (PDF)

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

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

Use this answer key to score the integer exponents test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.EE.A.1

Integer exponents test answers: worked solutions

Question 1 – Use the rules [4 pts]

\(5^{6}\)
\(7^{3} = 343\)
\(3^{6}\)
1

Scoring: 1 point for each correct part.

Question 2 – Negative exponents [3 pts]

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

\(2^{-1} = \frac{1}{2}\) and \(2^{-2} = \frac{1}{4}\).
\(10^{-2} = \frac{1}{100} = 0.01\).

Scoring: Part a: 1 point for each fraction. Part b: 1 point.

Question 3 – Expand and count [2 pts]

5^2 × 5^3 = 5^5

\(5^{2} \cdot 5^{3} = 5^{5} = 3{,}125\).

Scoring: 1 point for \(5^{5}\). 1 point for 3,125.

Question 4 – Fractions [2 pts]

Flip: \(\left(\frac{4}{3}\right)^{2} = \frac{16}{9}\).

\(\frac{16}{9}\)

Scoring: 1 point for flipping the fraction. 1 point for \(\frac{16}{9}\).

Question 5 – Multi-step [3 pts]

Numerator: \(3^{-2+7} = 3^{5}\). Then \(3^{5-2} = 3^{3}\).

\(3^{3} = 27\)

Scoring: 1 point for numerator \(3^{5}\). 1 point for \(3^{3}\). 1 point for 27.

Question 6 – Find the exponent [2 pts]

Subtract exponents: \(n – 3 = -2\), so \(n = 1\).

Scoring: 1 point for the equation \(n – 3 = -2\). 1 point for \(n = 1\).

Question 7 – Doubling [2 pts]

After \(w\) weeks: \(2^{w}\) thousand.

\(2^{8} = 256\).

256 thousand followers

Scoring: 1 point for \(2^{w}\). 1 point for 256 thousand.

Question 8 – Explain [2 pts]

A negative exponent means a reciprocal, not a product with a negative sign. \(5^{-2} = \frac{1}{5^{2}} = \frac{1}{25}\).

Scoring: 1 point for the explanation. 1 point for \(\frac{1}{25}\).

Total score

Total

20 points

Key facts behind this integer exponents test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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