Exponents and Roots
Exponent notation; evaluate powers; negative bases; decimal/fractional bases; multiplication law (aᵐ×aⁿ=aᵐ⁺ⁿ); division law (aᵐ÷aⁿ=aᵐ⁻ⁿ); power rule ((aᵐ)ⁿ=aᵐⁿ); square and cube roots; solve equations.
16 worksheetsRead the explainer →
- 1Understanding ExponentsInterpret exponential notation as repeated multiplication and evaluate simple powers.adaptive
- 2Evaluate PowersEvaluate powers with various bases and exponents.adaptive
- 3Solve Equations with Variable ExponentsFind the unknown base or exponent in b^x = n.adaptive
- 4Powers with Negative BasesDistinguish (-2)⁴ = 16 from -2⁴ = -16; evaluate powers with negative bases.adaptive
- 5Powers with Decimal and Fractional BasesEvaluate powers with decimal or fractional bases, e.g. (1/2)³ = 1/8.adaptive
- 6Multiplication with ExponentsApply aᵐ × aⁿ = aᵐ⁺ⁿ (NEW v9).adaptive
- 7Division with ExponentsApply aᵐ ÷ aⁿ = aᵐ⁻ⁿ (NEW v9).adaptive
- 8Multiplication and Division with Exponents CombinedApply both multiplication and division exponent laws in the same expression.adaptive
- 9Power RuleApply (aᵐ)ⁿ = aᵐⁿ (NEW v9).adaptive
- 10Evaluate Expressions Using Properties of ExponentsSimplify and evaluate using all three exponent laws.adaptive
- 11Identify Equivalent Expressions Involving Exponents IIdentify equivalent expressions using multiplication and division laws.adaptive
- 12Identify Equivalent Expressions Involving Exponents IIIdentify equivalent expressions using the power rule and combined laws.adaptive
- 13Square Roots of Perfect SquaresFind the square root of perfect squares up to 225.adaptive
- 14Estimate Square RootsEstimate √n between consecutive integers for non-perfect squares.adaptive
- 15Cube Roots of Perfect CubesFind cube roots of perfect cubes (∛8 = 2 through ∛1000 = 10).adaptive
- 16Solve Equations Involving Squares, Cubes and RootsSolve x² = 25, x³ = 27, √x = 4 and similar equations.adaptive