If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression
1. (7 * 7 * 7) * (7 * 7 * 7) * ( 7 * 7 * 7) * ( 7 * 7 * 7 ) * ( 7 * 7 * 7 )
2. ( 7^10)^5
3. (7 * 7 * 7 * 7 * 7)^10
4. (7^18)^3
The Power Rule of Exponents states that when raising a power to another power, you multiply the exponents.
In this case, 7^15 can be simplified using the Power Rule of Exponents by multiplying the exponents together.
So the correct expanded equivalent expression would be:
(7 * 7 * 7 * 7 * 7)^3
Answer: 3. (7 * 7 * 7 * 7 * 7)^10
The simplified form of the expression 7^15 using the Power Rule of Exponents would be option 1: (7 * 7 * 7) * (7 * 7 * 7) * ( 7 * 7 * 7) * ( 7 * 7 * 7 ) * ( 7 * 7 * 7 ).
To simplify an expression using the Power Rule of Exponents, we need to multiply the exponents. The Power Rule states that when we have an exponent raised to another exponent, we multiply the exponents together.
So, given the expression 7^15, let's examine each option to find the one that follows the Power Rule:
1. (7 * 7 * 7) * (7 * 7 * 7) * (7 * 7 * 7) * (7 * 7 * 7) * (7 * 7 * 7)
The exponents in this option are not multiplied together. Therefore, it does not follow the Power Rule.
2. (7^10)^5
According to the Power Rule, we should multiply the exponents together. Here, we have (7^10)^5, so we can multiply 10 (the exponent of 7^10) by 5 (the exponent raised to), resulting in 7^50. This option follows the Power Rule, and it is the correct expanded equivalent expression.
3. (7 * 7 * 7 * 7 * 7)^10
This option has multiple terms inside the parentheses multiplied together. Therefore, it does not follow the Power Rule.
4. (7^18)^3
Similar to option 2, we have (7^18)^3. Applying the Power Rule, we multiply 18 by 3 to get 7^54. However, it is crucial to note that this expression is not equivalent to 7^15, as the exponent is different.
In conclusion, the expanded equivalent expression that follows the Power Rule of Exponents for 7^15 is option 2: (7^10)^5.