Exponent Rules Checker: Write Powers Out the Long Way

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Opens on Chapter 16’s example: 2³ × 2⁴: three twos times four twos.

Base

First exponent

Second exponent

Operation

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Enter your numbers, then press Work it out.

How it works

aᵐ means m copies of a multiplied together. Multiplying aᵐ by aⁿ strings m copies and n copies into one row of m + n, so exponents add. Dividing cancels n copies from the top against the bottom, leaving m − n. A power of a power, (aᵐ)ⁿ, is n groups of m copies: m × n. Run the dividing rule down past zero and a⁰ = 1, a⁻¹ = 1 ÷ a, a⁻² = 1 ÷ a², and so on. Adding powers has no shortcut: 2³ + 2⁴ is 8 + 16, not 2⁷.

From the book, Chapter 16. 2³ × 2⁴ = 2⁷ = 128 (adding them gives only 24); 5⁶ ÷ 5⁴ = 5² = 25; (3²)³ = 3⁶ = 729; 10⁻³ = 0.001; 2¹⁰ = 1,024, the computer “thousand”. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.