Example: $x^3 \times x^4 = x^{3+4} = x^7$

Quotient Rule

When dividing powers with the same base, subtract exponents: $\frac{a^m}{a^n} = a^{m-n}$

Example: $\frac{x^7}{x^3} = x^{7-3} = x^4$

Power Rule

When raising a power to a power, multiply exponents: $(a^m)^n = a^{mn}$

Example: $(x^3)^4 = x^{3 \times 4} = x^{12}$

Zero Exponent

Any non-zero number to the zero power equals 1: $a^0 = 1 \quad (a \neq 0)$

Example: $5^0 = 1$

Negative Exponent

A negative exponent means reciprocal: $a^{-n} = \frac{1}{a^n}$

Example: $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$

Step 2: Quotient rule $\frac{x^{12}}{x^7} = x^{12-7} = x^5$

Answer: $x^5$

Step 2: Divide $\frac{16x^{12}}{4x^5} = \frac{16}{4} \times \frac{x^{12}}{x^5} = 4x^7$

Answer: $4x^7$