Evaluate powers with integer exponents, including zero and negative exponents, for integers, fractions, and terminating decimals, while attending to parentheses, signs, and order of operations. Apply exponent laws for products, quotients, powers of powers, products, and quotients to simplify numerical and algebraic expressions with integer exponents, including zero and negative exponents for nonzero bases. Determine exact principal square and cube roots of familiar perfect powers and estimate non-perfect square roots using nearby perfect squares, bounding values to the tenths or hundredths when appropriate.
On this page:
- Master skills like “Estimate square roots”, “Apply the power-of-a-power rule”, and “Apply exponent laws for products” with unlimited, free practice problems
- Download (or modify) free worksheets on Powers, Roots, and Exponents you can use at home or in class with practice problems across all skills in this group including “Apply exponent laws for quotients”, “Apply the power-of-a-product rule”, “Apply the power-of-a-quotient rule”.
- Start working on adaptive units like “Exponents - Multiplication and Division - Advanced” or “Exponents - Multiplication and Division - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Powers, Roots, and Exponents: Individual Skills
Master 10 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 exponent laws for products
- Apply exponent laws for quotients
- Apply the power-of-a-power rule
- Apply the power-of-a-product rule
- Apply the power-of-a-quotient rule
- Determine square roots of perfect squares
- Estimate square roots
- Evaluate powers with integer exponents
- Simplify expressions using exponent laws
- Simplify numerical expressions involving exponents and roots
Practice 'Apply exponent laws for products'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 9 'Powers, Roots, and Exponents' Worksheet
Print this free 'Powers, Roots, and Exponents' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Apply exponent laws for products
- Apply exponent laws for quotients
- Apply the power-of-a-power rule
- Apply the power-of-a-product rule
- Apply the power-of-a-quotient rule
- Determine square roots of perfect squares
- Estimate square roots
- Evaluate powers with integer exponents
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Powers, Roots, and Exponents) through scaffolded problems that grow in difficulty as concepts are understood.