Problem 90 - College Algebra Essentials

Question

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $$\left(1.4 \times 10^{15}\right)\left(3 \times 10^{-11}\right)$$

Step-by-Step Solution

Answer

The answer is \(4.2 \times 10^4\).

Step 1: Multiply the Decimal Factors

The first step is to multiply the decimal factors. In this case, that's \(1.4 \times 3 = 4.2\).

Step 2: Multiply the Powers of 10

Next, multiply the powers of 10. When you multiply numbers with the same base, you can simply add the exponents, i.e., \(10^{15} \times 10^{-11} = 10^{15+(-11)} = 10^4\).

Step 3: Write the Final Answer in Scientific Notation

The final answer, in scientific notation, is the product of the quantities computed in steps 1 and 2. So, the answer is \(4.2 \times 10^4\).