Final answer:
The question pertains to scientific notation, which expresses large or small numbers compactly with a coefficient and a power of ten.
Step-by-step explanation:
When multiplying two numbers in scientific notation, we multiply the coefficients and add the exponents. In this case, to multiply 3456789 by 123456789098765432123456789098765432, we multiply 3.456789 by 1.23456789098765432123456789098765432 and add the exponents 10^6 and 10^38. The result is 4.26478113 x 10^44, which can be written as 426478113 x 10^36. Exponents are added when multiplying powers of ten, and understanding calculator input for scientific notation is essential.
The student's question involves large numbers and scientific notation. Scientific notation is a way to express very large or very small numbers in a more compact form. It consists of a coefficient (a number between 1 and 10) and a power of ten. For example, the number 306,000 is written as 3.06 × 105. When calculating with scientific notation, one must add the exponents when multiplying powers of ten. For instance, (4.506 × 104) × (1.003 × 102) is calculated as 4.506 × 1.003 × 104+2, which results in approximately 4.517518 × 106 without using a calculator. Understanding how to properly enter these numbers into a calculator is essential, especially for fields like chemistry where this notation is commonly used.