Exponent Calculator – Powers & Negative Exponents

Exponentiation is repeated multiplication: 2¹⁰ means ten factors of 2, which multiplies out to 1024 — the size of 1 KiB in bytes and the reason binary memory sizes look so tidy. Negative exponents invert the base: 5⁻² = 1/5² = 1/25 = 0.04, and 2⁻¹⁰ = 1/1024 ≈ 0.000977. The zero rule states a⁰ = 1 for every nonzero base, so 999⁰ = 1. The calculator also applies the product rule aᵐ·aⁿ = aᵐ⁺ⁿ (2³·2⁴ = 2⁷ = 128) and the power rule (aᵐ)ⁿ = aᵐⁿ ((3²)³ = 3⁶ = 729), printing each expansion so you can verify every step by hand. Fractional exponents convert to roots: 8^(1/3) = 2.

1. 1

   Enter base and exponent

   Type values like 2 and 10, or a negative exponent such as -2

2. 2

   Handle the sign

   Negative n flips the base: a⁻ⁿ is computed as 1/aⁿ

3. 3

   Compute the power

   Repeated multiplication builds the exact result

4. 4

   Review the expansion

   Each intermediate product is listed for verification

• 1

  2¹⁰ = 1024, not 1000 — the binary/decimal gap that separates KiB from kB

• 2

  A negative exponent never makes the result negative; it makes it a fraction

• 3

  0⁰ is undefined; every other base to the power 0 equals 1

• Computing (-2)² as -4; the even power makes it +4

• Believing a⁻ⁿ is negative — it is the reciprocal 1/aⁿ

• Adding exponents of different bases: 2³·3² is 72, not 6⁵

• Assuming (a+b)ⁿ = aⁿ+bⁿ; (1+1)² = 4, not 2