Final answer:
The first step in the order of operations is to address grouping symbols, followed by exponents. Multiplying exponents involves adding the exponents of like bases, and division involves subtracting them. These rules also apply when multiplying or dividing numbers in scientific notation.
Step-by-step explanation:
In the order of operations, grouping symbols such as parentheses, brackets, or braces, come first. Following this rule, you would next address any exponents before proceeding to handle multiplication and division (from left to right), and finally addition and subtraction (also from left to right).
When dealing with exponents in particular, if we are multiplying exponentiated terms, we first multiply the coefficients (the numbers in front of the bases) and then add the exponents of like bases together. In contrast, when dividing exponentiated terms, we divide the coefficients and subtract the exponents of like bases. Scientific notation simplifies this process: when multiplying numbers in scientific notation, we multiply the significant figures (N-values) and add the exponents; when dividing, we do the opposite by dividing the significant figures and subtracting the exponents.
As an example, for multiplication: 32 × 33 = 3(2+3) = 35. For division: 106 / 103 = 10(6-3) = 103.