Final answer:
The question pertains to High School level Mathematics, with an emphasis on evaluating numerical expressions using calculators, simplifying results into proper scientific notation, and converting numbers between scientific and standard notation.
Step-by-step explanation:
The subject of the given question appears to be simplification of numerical expressions and operating with scientific notation, which falls under the Mathematics curriculum. The grade level is likely High School, based on the type of calculations and understanding of scientific notation required to perform these tasks.
When using a calculator to evaluate expressions and convert them into proper scientific notation, the process involves calculating the result and then adjusting the decimal place to express the number as a product of a number between 1 and 10 multiplied by a power of ten. Here are the steps to follow for the given problems:
- For the expression (9.09 × 10^8) ÷ [(6.33 × 10^9) × (4.066 × 10⁻7)], start by multiplying the divisor's components, then divide the dividend by the result, and lastly convert the final number into scientific notation.
- To solve 9,345 × 34.866 ÷ 0.00665, multiply 9,345 by 34.866, then divide the product by 0.00665, and express the result in proper scientific notation.
As for converting numbers from scientific notation to standard notation, move the decimal point to the right for positive exponents and to the left for negative exponents, counting the spaces equal to the absolute value of the exponent. For example:
- 7.11 × 10^-2 in standard notation would be 0.0711.
- 9.18 × 10^2 in standard notation would be 918.
Finally, with the expression (74)³, calculate by cubing the number 74, resulting in (7× 7× 7)×(7× 7× 7)×(7× 7× 7), which is equivalent to 7¹² based on the rule (x^a)^b = x^(a·b).