Exponent Rules

Exponent Rules

Product Rule

• When multiplying terms with the same base, keep the base and add the exponents.
• Formula: $b^m \cdot b^n = b^{m+n}$
• Example: If you have $b^3 \cdot b^2$, the result is $b^{3+2} = b^5$

Quotient Rule

• When dividing terms with the same base, keep the base and subtract the exponents.
• Formula: $\frac{b^m}{b^n} = b^{m-n}$
• Example: If you have $\frac{b^5}{b^2}$, the result is $b^{5-2} = b^3$

Power of One Rule

• Any base number to the power of 1 stays the base number.
• Formula: $b^1 = b$
• Example: $b^1 = b$

Power of Power Rule

• When raising a base with an exponent to another power, keep the base and multiply the exponents.
• Formula: $(b^m)^n = b^{m \cdot n}$
• Example: If you have $(b^2)^3$, the result is $b^{2 \cdot 3} = b^6$

Negative Exponent Rule

• Any base number to the power of a negative number is equivalent to the reciprocal of the base raised to the positive exponent.
• Formula: $b^{-n} = \frac{1}{b^n}$
• Example: If you have $b^{-2}$, the result is $\frac{1}{b^2}$

Zero Power Rule

• Any base number to the power of zero equals 1.
• Formula: $b^0 = 1$
• Example: If you have $b^0$, the result is $1$