Exponents Practice

Powers, roots, and scientific notation

Exponents are a shorthand way to express repeated multiplication. Instead of writing 2 × 2 × 2 × 2 × 2, we write 2⁵. Understanding exponent rules is essential for algebra, science, and working with very large or very small numbers.

Exponent Rules

• Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ (same base, add exponents)
• Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (same base, subtract exponents)
• Power rule: (aᵐ)ⁿ = aᵐˣⁿ (multiply exponents)
• Zero exponent: a⁰ = 1 (any non-zero base to the zero power is 1)
• Negative exponent: a⁻ⁿ = 1/aⁿ (flip to a fraction)

Scientific Notation

Scientific notation uses powers of 10 to express very large or very small numbers compactly. For example, 93,000,000 miles (distance to the Sun) becomes 9.3 × 10⁷. The number 0.000001 becomes 1 × 10⁻⁶. This notation is standard in science, engineering, and computing.

Square Roots and Radicals

The square root of a number is the value that, when multiplied by itself, gives the original number. √25 = 5 because 5 × 5 = 25. Radicals extend this to cube roots (∛), fourth roots, and beyond. Understanding radicals is crucial for the Pythagorean theorem, quadratic equations, and distance calculations.

Coming Soon

Our exponents practice engine will include rule application drills, scientific notation conversion, simplification exercises, and radical operations — all with instant feedback.