Apply the product, quotient, power-of-a-power, power-of-a-product, and power-of-a-quotient rules to simplify numerical and algebraic expressions with integer exponents, including expressions in scientific notation. Interpret zero exponents as 1 for nonzero bases and negative integer exponents as reciprocals, while preserving restrictions such as nonzero denominators and excluding $0^0$. Perform multiplication, division, addition, and subtraction in scientific notation by combining coefficients and powers of 10, using common powers when necessary, and renormalizing results to $1 \le |a| < 10$.