8th Grade Properties of Integer Exponents Worksheet (PDF)

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

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

These 21 problems practice the properties of integer exponents, including zero and negative exponents (Common Core 8.EE.A.1). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items combine several rules and use exponents in word problems. Use the answer key afterwards to check every step.

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

Integer exponents worksheet: exercises 1 to 10

Exercise 1 – Product rule

Use the product rule to write \(5^{3} \cdot 5^{4}\) as one power, then evaluate.

Exercise 2 – Quotient rule

Simplify \(\frac{5^{7}}{5^{4}}\) and evaluate.

Exercise 3 – Power of a power

Simplify \(\left(2^{3}\right)^{2}\) and evaluate.

Exercise 4 – Zero exponent

Evaluate \(7^{0}\) and \(\left(-12\right)^{0}\).

Exercise 5 – Count the factors

2^3 × 2^2 = 2^5

Write the product shown as one power of 2.

Exercise 6 – Negative exponent

Each step to the right divides by 3, so the exponent drops by 1.

Complete the pattern: write \(3^{-1}\) and \(3^{-2}\) as fractions.

Exercise 7 – Powers of ten

Each step to the right divides by 10, so the exponent drops by 1.

Use the pattern to write \(10^{-2}\) as a fraction and as a decimal.

Exercise 8 – Mixed exponents

Simplify \(2^{5} \cdot 2^{-3}\) and evaluate.

Exercise 9 – Negative power of a power

Write \(\left(3^{2}\right)^{-1}\) with a positive exponent and evaluate.

Exercise 10 – Quotient with a negative result

Simplify \(\frac{4^{2}}{4^{5}}\) and give the result as a fraction.

Exercises 11 and up

Exercise 11 – Power of a product

Evaluate \(\left(2 \cdot 5\right)^{3}\) in two ways: first inside the parentheses, then by using \(2^{3} \cdot 5^{3}\).

Exercise 12 – Fraction to a negative power

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

Exercise 13 – Several rules

Simplify \(\frac{5^{-3} \cdot 5^{6}}{5^{2}}\).

Exercise 14 – Write as a power

Write \(\frac{1}{81}\) as a power of 3 with a negative exponent.

Exercise 15 – Power of a power with negatives

Simplify \(\left(2^{-3}\right)^{2} \cdot 2^{9}\) and evaluate.

Exercise 16 – Nested rules

Simplify \(\frac{4^{2} \cdot 4^{-5}}{4^{-1}}\) and write it as a fraction.

Exercise 17 – Find the exponent

Find \(n\) so that \(3^{n} \cdot 3^{5} = 3^{2}\).

Exercise 18 – Bacteria growth

Cells double each hour.

A lab culture starts with 1 cell and doubles every hour, so after \(t\) hours there are \(2^{t}\) cells. How many cells are there after 10 hours? How many times as many cells are there after 12 hours as after 10 hours?

Exercise 19 – Computer storage

A kilobyte is about \(2^{10}\) bytes and a gigabyte is about \(2^{30}\) bytes. How many kilobytes make a gigabyte? Write the answer as a power of 2 and as a number.

Exercise 20 – Square tile

Ethan’s square tile has side 3² inches.

Ethan’s square tile has side \(3^{2}\) inches. Write its area as a power of 3 and find the area in square inches.

Exercise 21 – Find the error

Priya simplified \(\left(5^{2}\right)^{3}\) as \(5^{5}\). Describe her error and give the correct value.

Key facts behind this integer exponents worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the integer exponents worksheet as a PDF with the button below and keep it with your notes.

All Grade 8 chapters: Grade 8 math.

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