Final answer:
The student appears to be inquiring about scientific notation and exponent rules, but the original question is unclear due to typos. In scientific notation, arithmetic operations involve multiplying or dividing the base numbers and adding or subtracting the exponents, with care for significant figures.
Step-by-step explanation:
The student's question seems to be about recognizing and manipulating expressions, possibly involving scientific notation and exponent rules. However, due to typos in the question, it's unclear what the original question is, so I cannot provide an accurate answer. The reference material provided relates to performing arithmetic operations with numbers expressed in scientific notation and applying exponent rules. When multiplying numbers in scientific notation, you multiply the base numbers and add the exponents. When dividing, you divide the base numbers and subtract the exponents. Care must be taken to express the final answer in proper scientific notation with the correct number of significant figures, and the base number usually between 1 and 10.
One common example is moving the decimal point to convert from scientific notation to standard form, and vice versa. A number like 1.6 \(\times\) 10\(^2\) becomes 160 when converting to standard form, as you move the decimal two places to the right. Alternatively, a number such as 0.024 is expressed as 2.4 \(\times\) 10\(^{-2}\) in scientific notation, as the decimal point is moved two places to the left.
Exponent rules are crucial in these calculations. When two exponents with the same base are multiplied, their exponents are added. When they are divided, the exponents are subtracted. Additionally, when a number is raised to a power, the exponent is multiplied by the power. Proper application of these rules is essential for reaching the correct answers.