If the expression 7^(15) was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression? (1 point)
(7^(18))^(3)
(7*7*7)*(7*7*7)*(7*7*7)*(7*7*7)*(7*7*7)
(7*7*7*7*7)^(10)
(7^(10))^(5)
The correct choice would be (7^(10))^(5).
The correct answer would be (7^(18))^(3).
To simplify the expression 7^(15) using the Power Rule of Exponents, we need to remember that when we have a power raised to another power, we multiply the exponents.
The Power Rule of Exponents states that (a^b)^c = a^(b*c), where "a" is the base, "b" is the exponent of the base, and "c" is the exponent of the entire expression.
So, let's look at the options:
1) (7^(18))^(3)
This option is using the Power Rule correctly. We have (7^(18)) raised to the power of 3. According to the Power Rule, we multiply the exponents, so (7^(18))^(3) is equal to 7^(18*3) = 7^(54).
2) (7*7*7)*(7*7*7)*(7*7*7)*(7*7*7)*(7*7*7)
This option is not simplified and does not use the Power Rule. It simply expands the expression as repeated multiplication.
3) (7*7*7*7*7)^(10)
This option is not equivalent to the original expression. It simplifies to (7^5)^(10), which is equal to 7^(5*10) = 7^(50).
4) (7^(10))^(5)
This option uses the Power Rule correctly. We have (7^(10)) raised to the power of 5. According to the Power Rule, we multiply the exponents, so (7^(10))^(5) is equal to 7^(10*5) = 7^(50).
So, the expanded equivalent expression, if we simplify 7^(15) using the Power Rule of Exponents, is (7^(18))^(3) or option 1.