If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression
The Power Rule of Exponents states that for any real number a and positive integers m and n, (a^m)^n is equal to a^(m * n).
Therefore, if the expression 7^15 was simplified using the Power Rule of Exponents, the expanded equivalent expression would be 7^(15 * 1), which equals 7^15.
The Power Rule of Exponents states that if you have a base raised to an exponent, and that expression is raised to another exponent, you can multiply the exponents together.
In this case, we have the expression 7^15. To apply the Power Rule of Exponents, we need to look for another exponent. Is there another exponent outside of the 7^15?
If there is no other exponent, then the expression 7^15 is already in its simplest form and there is no need for further expansion.
To simplify the expression 7^15 using the Power Rule of Exponents, we can rewrite 7^15 as (7^3)^5. According to the Power Rule, when raising a power to another power, we multiply the exponents.
So, (7^3)^5 becomes 7^(3*5), which simplifies to 7^15.
Since we are looking for an expanded equivalent expression, we need to distribute the exponent 15 to each term inside parentheses.
Therefore, 7^(3*5) can be written as 7^3 * 7^3 * 7^3 * 7^3 * 7^3.
So, an expanded equivalent expression for 7^15 using the Power Rule of Exponents is 7^3 * 7^3 * 7^3 * 7^3 * 7^3.