Which of the following correctly used the Product Rule of Exponents to simplify the expression 100 ^ 8 * 100 ^ 7 (1 point) 100 ^ 56; 10000 ^ 15; 100 ^ 15; 200 ^ 15
The correct answer is 100^15.
When using the Product Rule of Exponents, we add the exponents when multiplying two powers with the same base. In this case, both exponents are positive, so we add them together: 8 + 7 = 15.
Therefore, 100^8 * 100^7 simplifies to 100^15.
To simplify the expression using the Product Rule of Exponents, we need to add the exponents when multiplying two bases with the same base value.
The expression 100^8 * 100^7 can be simplified as (100*100)^8 * 100^7.
Now, simplify (100*100) to get 10,000, and rewrite the expression: 10,000^8 * 100^7.
We can further simplify this by applying the Power Rule of Exponents, which states that when raising an exponent to another exponent, you simply multiply the exponents.
10,000^8 * 100^7 becomes 10^(8*2) * 100^7, which is 10^16 * 100^7.
Finally, apply the Product Rule of Exponents, which says that when multiplying two bases with the same base value, you add the exponents.
So, 10^16 * 100^7 becomes 10^16 * 10^14, by adding the exponents (7 + 2 = 14).
Simplifying further, we use the Power Rule of Exponents to add the exponents: 10^(16 + 14), which is 10^30.
Therefore, the correct answer is 10^30.
To simplify the expression "100^8 * 100^7" using the Product Rule of Exponents, we need to remember that the rule states that when multiplying two numbers with the same base, you can add their exponents.
In this case, the base is 100, and the exponents are 8 and 7. Applying the Product Rule of Exponents, we add the exponents:
8 + 7 = 15
Therefore, the expression simplifies to "100^15".
So, the correct answer is "100^15".