Interpret and evaluate powers with whole-number exponents, including integer and negative bases, zero exponents, parentheses, and the product, quotient, and power-of-a-power rules, without using negative or fractional exponents. Recognize perfect squares and determine their principal square roots from 0 through 225, and estimate nonperfect square roots between consecutive integers whose squares bound them. Write large and small nonzero numbers in scientific notation and convert between scientific and standard form, using with and interpreting positive and negative integer exponents through place value.
On this page:
- Master skills like “Recognize perfect squares”, “Apply the power-of-a-power rule”, and “Apply the product rule for powers” with unlimited, free practice problems
- Download (or modify) free worksheets on Powers, Roots, and Scientific Notation you can use at home or in class with practice problems across all skills in this group including “Apply the quotient rule for powers”, “Evaluate powers with integer bases”, “Determine square roots of perfect squares”.
- Start working on adaptive units like “Measurement - Units Advanced - Metric” or “Scientific Notation - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Powers, Roots, and Scientific Notation: Individual Skills
Master 11 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Apply the power-of-a-power rule
- Apply the product rule for powers
- Apply the quotient rule for powers
- Convert between scientific notation and standard form
- Determine square roots of perfect squares
- Distinguish negative powers from powers with negative bases
- Estimate square roots between consecutive integers
- Evaluate powers with integer bases
- Interpret powers with whole-number exponents
- Recognize perfect squares
- Write large and small numbers in scientific notation
Practice 'Apply the power-of-a-power rule'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
Hover a skill above to start practicing.
Download/Modify Free Grade 8 'Powers, Roots, and Scientific Notation' Worksheet
Print this free 'Powers, Roots, and Scientific Notation' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Apply the power-of-a-power rule
- Apply the product rule for powers
- Apply the quotient rule for powers
- Convert between scientific notation and standard form
- Determine square roots of perfect squares
- Distinguish negative powers from powers with negative bases
- Estimate square roots between consecutive integers
- Evaluate powers with integer bases
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Powers, Roots, and Scientific Notation) through scaffolded problems that grow in difficulty as concepts are understood.