If the expression 7^15 was simplified using the power rule of exponents which of the following would be an expanded equivalent expression?
A. (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7)
B. (7•7•7•7•7)^10
C. (7^18)^3
D. (7^10)^5
The power rule of exponents states that when raising a power to another power, you multiply the exponents.
In this case, the expression 7^15 can be simplified using the power rule as (7^5)^3.
Therefore, the expanded equivalent expression would be (7•7•7•7•7)^3, which corresponds to option B. (7•7•7•7•7)^10.
To simplify 7^15 using the power rule of exponents, we can multiply the exponents when the bases are the same.
The power rule of exponents states that if we have a number raised to a power, and that whole expression is raised to another power, we can multiply the exponents together.
Using this rule, when we simplify 7^15, we can express it as (7^1)^15, which becomes 7^15.
Now, let's look at the options given:
A. (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7)
This option is simply expanding the expression by multiplying 7 by itself 15 times, which results in (7^15). So, option A is correct.
B. (7•7•7•7•7)^10
This option is raising 7 to the power of 10 and not expanding the expression. So, option B is not correct.
C. (7^18)^3
This option raises 7 to the power of 18, and then raises the result to the power of 3. It does not represent the expanded equivalent expression. So, option C is not correct.
D. (7^10)^5
This option raises 7 to the power of 10, and then raises the result to the power of 5. It does not represent the expanded equivalent expression. So, option D is not correct.
Therefore, the expanded equivalent expression for 7^15 using the power rule of exponents is option A: (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7) • (7•7•7).
The power rule of exponents states that when raising an exponent to another exponent, you multiply the exponents.
In this case, the expression 7^15 can be simplified using the power rule of exponents as follows:
7^15 = (7^5)^3
Therefore, the correct expanded equivalent expression would be:
D. (7^10)^5