Final answer:
To solve the expression, multiply the coefficients and add the exponents; then combine the results to get the final answer in scientific notation. The final answer is 2.93 × 10³⁷.
Step-by-step explanation:
The student has asked to solve the expression (6.7×10⁻¹¹ )(6×10²⁴)(7.4×10²²)(3.84×10⁻¹) by multiplying these numbers together. To do this, we first multiply the decimal parts and then add the exponents according to the rules of exponentiation.
Multiplying the coefficients (non-exponential parts) gives us:
6.7 × 6 × 7.4 × (3.84 × 3.84) = 6.7 × 6 × 7.4 × 14.7456
Adding the powers of ten gives us:
10⁻¹¹ + 10²⁴ + 10²² + (2 × 10¹) = 10³⁵
The product of the coefficients is 293.043648, and the sum of the exponents is 35. Now, we combine these two results to get the final answer in proper scientific notation:
293.043648 × 10³⁵
After adjusting the coefficient to have only one non-zero digit to the left of the decimal point, we get:
2.93 × 10³⁷
This is our final answer in proper scientific notation.