if the expression 7^15 was simplified using the power rule of exponents which of the following would be an expanded expanded equivalent
expression
(7.7.7.7.7)
(7^10)^5
(7^10)^5
(7^18)^3
(7.7.7)(7.7.7)(7.7.7)(7.7.7)(7.7.7)
The correct answer would be (7^10)^5.
The correct option would be (7^10)^5.
To simplify 7^15 using the power rule of exponents, we can multiply the exponents when raising a power to another power.
So, 7^15 can be written as (7^10)^5.
To simplify the expression 7^15 using the power rule of exponents, we need to multiply the exponent (15) by the exponent of the base (7). The power rule states that when you multiply exponential expressions with the same base, you add their exponents.
So, 7^15 can be simplified as (7^1)(7^14), since 15 = 1 + 14.
Now, let's look at the answer choices provided:
1) (7.7.7.7.7): This is just multiplying 7 five times, so it is equal to 7^5. Therefore, it is not the expanded equivalent of 7^15.
2) (7^10)^5: This is raising 7^10 to the power of 5. It is not the expanded equivalent of 7^15.
3) (7^10)^5: This is the same as the previous answer choice. It is also not the expanded equivalent of 7^15.
4) (7^18)^3: This is raising 7^18 to the power of 3. It is not the expanded equivalent of 7^15.
5) (7.7.7)(7.7.7)(7.7.7)(7.7.7)(7.7.7): This expression is equal to (7^3)(7^3)(7^3)(7^3)(7^3), which simplifies to (7^3)^5. This matches the expression (7^1)(7^14) we obtained earlier by applying the power rule of exponents. Therefore, the expanded equivalent expression is (7.7.7)(7.7.7)(7.7.7)(7.7.7)(7.7.7)