Exponent Rules

Basic Exponent Rules

	law	formula	explanation
	Identity Rule	$a^1 = a$	Any number raised to the power of 1 is itself
	Zero Exponent Rule	$a^0 = 1$	Any non-zero base raised to 0 is 1

Multiplication and Division Rules

	law	formula	explanation
	Product of Powers	$a^m \cdot a^n = a^{m+n}$	Add exponents when multiplying same base
	Quotient of Powers	$\frac{a^m}{a^n} = a^{m-n}$	Subtract exponents when dividing same base

Power Rules

	law	formula	explanation
	Power of a Power	$(a^m)^n = a^{mn}$	Multiply exponents when raising a power to another power
	Power of a Product	$(ab)^n = a^n \cdot b^n$	Distribute exponent across multiplied terms
	Power of a Quotient	$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$	Distribute exponent across division

Negative Exponents

	law	formula	explanation
	Negative Exponent Rule	$a^{-n} = \frac{1}{a^n}$	A negative exponent means reciprocal

Fractional Exponents

	law	formula	explanation
	Fractional Exponent Rule	$a^{\frac{m}{n}} = \sqrt[n]{a^m}$	Fractional exponents represent roots and powers