Write and evaluate numerical expressions involving whole-number exponents.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
An exponent is shorthand for repeated multiplication. Writing 2 × 2 × 2 × 2 × 2 is tedious; writing 2⁵ is quick, and it says that 2 is used as a factor 5 times, giving 32. Sixth graders write numerical expressions with whole-number exponents and evaluate them, including expressions where exponents sit alongside other operations, like 3 + 4² or 5 × 2³.
Two details matter a great deal. First, the exponent applies only to the number directly beneath it, so 5 × 2³ means 5 × 8, not 10³. Second, exponents come before multiplication, division, addition and subtraction in the order of operations, though anything in parentheses is done first: (3 + 1)² is 16, while 3 + 1² is 4. Students also meet special cases: any number to the power 1 is itself, and 10 to a power has a pattern of zeros that links to place value from fifth grade. Squares and cubes get their names from area and volume, which later connects to 6.G.A.2.
The most common error is 4³ = 12. Write out 4 × 4 × 4 = 64 until students see the exponent counts factors, not a multiplier.
In 3 × 2², only the 2 is squared, so the value is 12. Students who compute 6² = 36 have ignored the order of operations.
(1/2)² = 1/4 is smaller than 1/2. Squaring a number between 0 and 1 makes it smaller.
Evaluate 50 - 3 × 2³ + (4 + 1)².
Answer: The value is 51.
Folding a sheet of paper in half repeatedly gives a quick, memorable picture of powers of 2. Building squares and cubes from tiles and blocks explains the words 'squared' and 'cubed'.
When students practice order of operations, include expressions where getting the exponent step out of order changes the answer. Assessment items often ask students to identify the expression equal to a given power or to evaluate a mixed expression.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 81
3⁴ = 3 × 3 × 3 × 3 = 81.
Answer: D) 6⁵
6 is used as a factor 5 times, so the expression is 6⁵.
Answer: 50
Exponent first: 5² = 25. Then 2 × 25 = 50.
Answer: B) 4/9
(2/3)² = 2/3 × 2/3 = 4/9.
Answer: 16
Exponent: 2³ = 8. Division: 8 ÷ 4 = 2. Subtraction: 18 - 2 = 16.
Answer: D) 10,000
10⁴ = 10 × 10 × 10 × 10 = 10,000: a 1 followed by four zeros.
Answer: 0.008
0.2 × 0.2 = 0.04, and 0.04 × 0.2 = 0.008.
A full lesson with slides, activities and an exit ticket on whole-number exponents, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.EE.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn whole-number exponents into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. 6.EE.A.1 uses whole-number exponents only. Integer exponents, including negative ones, are part of grade 8 (8.EE.A.1).
After parentheses and before multiplication, division, addition and subtraction.