Certainly! Let's go through each question step by step:
1. (5.4*10^-1)(7*10^0)
- In this case, we are multiplying two numbers with bases of 10. The first term is 5.4 multiplied by 10 raised to the power of -1, and the second term is 7 multiplied by 10 raised to the power of 0.
- Multiplying the numbers, we get (5.4 * 7).
- Multiplying the exponents of 10, we add -1 and 0, which gives us 10^(-1 + 0) = 10^-1.
- Putting it all together, we have (5.4 * 7) * 10^-1 = 37.8 * 10^-1 = 3.78.
2. (5*10^3)(3.5*10^-1)
- Again, we are multiplying two numbers with bases of 10. The first term is 5 multiplied by 10 raised to the power of 3, and the second term is 3.5 multiplied by 10 raised to the power of -1.
- Multiplying the numbers, we get (5 * 3.5).
- Multiplying the exponents of 10, we add 3 and -1, which gives us 10^(3 + -1) = 10^2.
- Putting it all together, we have (5 * 3.5) * 10^2 = 17.5 * 10^2 = 1750.
3. (4.11*10^5)(8.65*10^-5)
- Similar to the previous questions, we have two numbers with bases of 10. The first term is 4.11 multiplied by 10 raised to the power of 5, and the second term is 8.65 multiplied by 10 raised to the power of -5.
- Multiplying the numbers, we get (4.11 * 8.65).
- Multiplying the exponents of 10, we add 5 and -5, which gives us 10^(5 + -5) = 10^0 = 1.
- Putting it all together, we have (4.11 * 8.65) * 10^0 = 35.5815 * 10^0 = 35.5815.
4. (8.31*10^-3)(6.6*10^-6)
- Again, we have two numbers with bases of 10. The first term is 8.31 multiplied by 10 raised to the power of -3, and the second term is 6.6 multiplied by 10 raised to the power of -6.
- Multiplying the numbers, we get (8.31 * 6.6).
- Multiplying the exponents of 10, we add -3 and -6, which gives us 10^(-3 + -6) = 10^-9.
- Putting it all together, we have (8.31 * 6.6) * 10^-9 = 54.846 * 10^-9 = 5.4846 * 10^-8.
Hope this clears up the explanations for you! Let me know if you have any more questions.