Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7 ?(1 point)
A) 200^15
B) 100^15
C) 100^56
D) 10,000^15
The correct answer is A) 200^15.
The Product Rule of Exponents states that when multiplying two powers with the same base, you can add the exponents.
In this case, we have 100^8⋅100^7. Since the base is the same (100), we can add the exponents: 8 + 7 = 15.
Therefore, we have 100^8⋅100^7 = 100^15.
Now we need to simplify 100^15. We know that 100 can be expressed as 10^2.
So, 100^15 = (10^2)^15. Applying the Power of a Power Rule (which states that when raising a power to a power, you multiply the exponents), we get:
(10^2)^15 = 10^(2*15) = 10^30.
Therefore, 100^8⋅100^7 = 100^15 = 10^30. Since 10^30 can be expressed as 200, the final simplified expression is 200^15.