Exponent & Power Calculator Pro
Solve standard powers (bx), exponent arithmetic rules (product, quotient, power-of-power), and discrete modular exponentiation.
Quick Presets:
Standard Power Calculation (bx)
Power Evaluation
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📝 Step-by-Step Mathematical Derivation:
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Product Rule: bx × by = b(x + y)
Quotient Rule: bx ÷ by = b(x − y)
Power of Power: (bx)y = b(x × y)
Negative Power: b−n = 1 / bn
The meaning of an exponent
An exponent indicates repeated multiplication of a base by itself: bn = b × b × ... × b (n times). For negative exponents, the operation inverts to reciprocal division: b−n = 1 / bn. For fractional exponents bm/n, the denominator represents the radical root (e.g. b1/2 = √b).
Frequently asked questions
What is an exponent?▶
An exponent says how many times to multiply a base by itself. In 2^5, the base 2 is multiplied 5 times: 2 × 2 × 2 × 2 × 2 = 32.
What is a negative exponent?▶
A negative exponent means the reciprocal of the positive power: b^-n = 1 / (b^n). For example, 2^-3 = 1/(2^3) = 1/8 = 0.125.
What is a fractional exponent?▶
A fractional exponent represents a radical root: x^(1/n) is the nth root of x. For example, 27^(2/3) = (³√27)² = 3² = 9.
What is any non-zero number to the power of zero?▶
Any non-zero number raised to the power of zero equals 1 (e.g., 5^0 = 1, 999^0 = 1).