Simplify powers with confidence. Compare exponent laws, steps, graphs, and exports. Master products, quotients, roots, and powers using guided results.
Use the rule selector to test products, quotients, powers, negatives, zeros, and fractional exponents with one interface.
The graph plots how the selected base behaves across exponent values generated from your current rule setup.
| Rule | Example Expression | Simplified Form | Value |
|---|---|---|---|
| Product Rule | 2^3 × 2^4 | 2^7 | 128 |
| Quotient Rule | 5^6 ÷ 5^2 | 5^4 | 625 |
| Power of a Power | (3^2)^4 | 3^8 | 6561 |
| Negative Exponent | 2^-3 | 1 / 2^3 | 0.125 |
| Fractional Exponent | 16^(1/2) | √16 | 4 |
Product Rule: a^m × a^n = a^(m + n)
Quotient Rule: a^m ÷ a^n = a^(m - n), where a ≠ 0
Power of a Power: (a^m)^n = a^(mn)
Power of a Product: (ab)^n = a^n b^n
Power of a Quotient: (a/b)^n = a^n / b^n, where b ≠ 0
Zero Exponent: a^0 = 1, where a ≠ 0
Negative Exponent: a^-n = 1 / a^n, where a ≠ 0
Fractional Exponent: a^(m/n) = n-th root of a^m
These rules turn complicated expressions into shorter forms while preserving the same mathematical value.
It combines powers with the same base during multiplication. You keep the base and add the exponents. For example, 2^3 × 2^4 becomes 2^7.
Use it when dividing powers that share the same base. Keep the base and subtract the denominator exponent from the numerator exponent.
A negative exponent means the factor moves across the fraction bar. So a^-n equals 1/a^n, provided the base is not zero.
It follows from the quotient rule. Dividing equal powers gives a^(m-m) = a^0, and the numeric division equals 1, so a^0 = 1.
A fractional exponent represents both a power and a root. For example, a^(3/2) means the square root of a^3, or equivalently, the cube of √a.
Yes. Decimal and fractional exponent values can be evaluated numerically. The step explanation still follows the selected exponent law where possible.
Some exponent expressions are undefined in real numbers. Examples include division by zero, zero raised to a negative power, and even roots of negative numbers.
The chart shows how the base changes as exponent values vary. It helps you compare rapid growth, decay, and reciprocal behavior visually.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.