8.EE.1 — Integer Exponents: Mixed Operations Practice
Practice applying properties of integer exponents, including positive, zero, and negative exponents, to simplify and generate equivalent numerical expressions.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Simplify each expression and write your answer in the space provided.
- 1.3² × 3³ =
- 2.5⁰ =
- 3.2⁻³ =
- 4.4³ ÷ 4¹ =
- 5.(2³)² =
- 6.7⁻² =
- 7.6² × 6⁰ =
- 8.10³ ÷ 10⁵ =
- 9.(3²)⁻¹ =
- 10.2⁴ × 2⁻² =
- 11.5² ÷ 5⁻¹ =
- 12.(4⁻²) =
- 13.9⁰ × 9² =
- 14.(2⁻¹)³ =
- 15.3³ × 3⁻³ =
- 16.10⁴ ÷ 10² =
- 17.(5²)⁰ =
- 18.2⁵ ÷ 2⁻¹ =
- 19.4⁻¹ × 4³ =
- 20.(3⁻²)² =
- 21.6³ ÷ 6³ =
- 22.2⁻⁴ × 2⁶ =
What this worksheet covers
There are 22 integers problems here — one page to work, one page of answers to check against — and Sets B and C repeat the layout with different numbers. The expressions carry exponents, so the order of operations decides the answer and several problems use mixed numbers, which have to be handled without dropping the whole-number part. Problems 8 and 15, for instance, are "10³ ÷ 10⁵" and "3³ × 3⁻³". Common Core 8.EE.1 is the slot this page fills.
Skills practised
At grade 8, integers is about integer exponents, the product, quotient and power rules, negative exponents and scientific notation, and this sheet takes one slice of that. The skill on the page: integer Exponents: Mixed Operations Practice. Concretely, the sheet tests whether a student can apply the order of operations to powers. Fifteen different answers appear across the 22 problems, so a student cannot copy one result down the page.
About the drill format
A drill is straight practice: 22 problems of the same kind, laid out across the page with working space under each — problem 8, "10³ ÷ 10⁵" is typical of the whole page. A page of one signed operation is where the sign rule stops being recited and starts being applied.
Set A, Set B and Set C
Set A is the sheet as it was first published on MathSheetLab, and Sets B and C were derived from it problem by problem: each number became a slot redrawn with the same shape, and every answer was recomputed exactly. Where Set A's problem 12 is "(4⁻²)", Set B's is "(6⁻²)".
How to use this worksheet
Expect twenty minutes or so of real attention for 22 problems. At grade 8, integers rewards care over speed — a rushed drill gets the arithmetic right and the signs or units wrong. If more than a third of the 22 problems come back wrong, stop and step back a grade in integers rather than assigning Set B.
One mistake to watch for
A negative exponent makes the result negative: 2^-3 is answered -8. Watch problem 15 of this drill — "3³ × 3⁻³" — for this one.
The minus sign is being attached to the value instead of inverting it.
Extend a table of powers of 2 downward past 2^0 and let the halving pattern show what the negative exponent does.
Other grade 8 integers formats
The same skill in the other formats available at this grade.
- Timed Drill — Grade 8 Multiplying Numbers in Scientific Notation, 16 problems
- Missing Number — Grade 8 Integers Missing Number, 24 problems
- Mixed Review — Grade 8 Repeating Decimals as Fractions, 16 problems
- Word Problems — Grade 8 Integers Word Problems, 10 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 7 Adding Rational Numbers — grade 7, 20 problems
Drill sheets in other grade 8 topics
No paywall and no account — download any set of this grade 8 integers drill, and the answers for all 22 problems are in the matching key.