Final answer:
The best estimate for the product (8.91×10²) (3.3×10¹²) in scientific notation is approximately 2.94×10¹⁴, meaning the power of ten is 14.
Step-by-step explanation:
The student asks to find the best estimate for the product of two numbers in scientific notation: (8.91×10²) (3.3×10¹²). To perform the multiplication, we multiply the coefficients (8.91 and 3.3) and add together the exponents of 10 (2 and 12).
The product of the coefficients 8.91 and 3.3 is approximately 29.403, which we can round to 29.4 to keep the coefficient between 1 and 10 for proper scientific notation.
The sum of the exponents is 2 + 12 = 14. Therefore, we write the product as approximately 2.94×10¹⁴, which in scientific notation means we need the power of ten to be 14.