What is the first step to multiply or divide numbers in standard form?

When working with numbers in standard form, the first step to multiplying or dividing them is to rearrange them in such a way that you can easily handle the significant figures (the numbers in front) and the powers of ten separately. This involves separating the coefficients (the front numbers) from the powers of ten so that you can manipulate each part according to the rules of multiplication or division.

By grouping the front numbers and the powers of ten, you set a clear path for the operations. For example, when multiplying, you can multiply the coefficients together and then add the exponents of the powers of ten. Conversely, when dividing, you still work with the coefficients separately from the powers of ten but you would then subtract the exponents.

This method organizes the calculation, making it simpler to apply the appropriate arithmetic operations correctly. It lays the groundwork for applying the rules of exponents efficiently once the coefficients are dealt with.