Laws for Same Base: For multiplication, add the indices (e.g., $2^3 \times 2^4 = 2^7$). For division, subtract the indices (e.g., $4^5 \div 4^3 = 4^2$).

Laws for Same Index: For multiplication, multiply the bases and keep the index (e.g., $2^3 \times 5^3 = 10^3$). For division, divide the bases and keep the index (e.g., $6^5 \div 3^5 = 2^5$).