1. Problem: Multiply and write each product in scientific notation. (a) Multiply $(4 \times 10^{-5})(2.1 \times 10^{-7})$. Formula: $ (a \times 10^m)(b \times 10^n) = (a \times b) \times 10^{m+n} $. Step 1: Multiply the coefficients: $4 \times 2.1 = 8.4$. Step 2: Add the exponents: $-5 + (-7) = -12$. Step 3: Write the product: $8.4 \times 10^{-12}$. (b) Multiply $(4 \times 10^{5})(6 \times 10^{7})$. Step 1: Multiply the coefficients: $4 \times 6 = 24$. Step 2: Add the exponents: $5 + 7 = 12$. Step 3: Write the product: $24 \times 10^{12}$. Step 4: Convert to proper scientific notation by expressing 24 as $2.4 \times 10^1$: $$24 \times 10^{12} = (2.4 \times 10^1) \times 10^{12} = 2.4 \times 10^{13}$$ Final answers: (a) $8.4 \times 10^{-12}$ (b) $2.4 \times 10^{13}$