Define: Exponent Rule for Multiplication of like bases:
Define: Words that tell you to multiply:
Define: What happens when you multiply by a large number? Define: What happens when you multiply by a small number?
Exponent Rule for Multiplication of like bases: This rule states that when you multiply two numbers with the same base, you add the exponents. It can be written as:
a^m * a^n = a^(m + n)
Words that tell you to multiply: Words that indicate multiplication include "times," "product," "multiply," "of," and the multiplication symbol (*).
What happens when you multiply by a large number: When you multiply by a large number, the resulting product becomes greater. For example, if you multiply 5 by 100, the product is 500.
What happens when you multiply by a small number: When you multiply by a small number, the resulting product becomes smaller. For example, if you multiply 5 by 0.01, the product is 0.05.
1. (5.4*10^-1)(7*10^0)=
2. (5*10^3)(3.5*10^-1)=
3. (4.11*10^5)(8.65*10^-5)=
4. (8.31*10^-3)(6.6*10^-6)=
1. (5.4*10^-1)(7*10^0) = (5.4*7) * (10^-1 * 10^0) = 37.8 * 10^-1 = 3.78
2. (5*10^3)(3.5*10^-1) = (5*3.5) * (10^3 * 10^-1) = 17.5 * 10^2 = 1750
3. (4.11*10^5)(8.65*10^-5) = (4.11*8.65) * (10^5 * 10^-5) = 35.5815 * 10^0 = 35.5815
4. (8.31*10^-3)(6.6*10^-6) = (8.31*6.6) * (10^-3 * 10^-6) = 54.846 * 10^-9 = 5.4846 * 10^-8
Could you please explain your answer more better for me please and thank you.
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.