What Are the Laws of Exponents in Math?

The laws of exponents consist of the power rule, product rule, quotient rule, zero rule, rules of one and rules of negative exponents. These tools prove useful for simplifying and manipulating mathematical expressions with exponents.

The power rule helps when raising a power to another power. The base of the expression stays the same, and the new exponent value is the product of the two exponent values.

The product rule of exponents applies when two exponential expressions with the same bases are multiplied. The expression can be simplified to one where the base stays the same, and the new exponent value is the sum of the two exponent values.

The quotient rule is similar to the product rule but is used when an exponential expression is divided by another with the same base. The simplified version has the same base, and the exponent is the difference between the dividend expression’s exponent and the divisor expression’s exponent.

The zero rule says that any number, except zero, raised to the power of zero equals one.

The rules of one say that any base number raised to the power of one equals itself and that the number one raised to any power equals one.

The rule of negative exponents allows simplification of bases raised to a negative number. They equal the reciprocal of the base raised to the opposite, positive power.