Which expression is correctly developed to use the Product Rule of Exponents? (1 point) 6 ^ 2 * 7 ^ 3 © (5 ^ 2) ^ 9; 32 ^ 7; 10 ^ 8 * 10 ^ 8
The correct expression to use the Product Rule of Exponents is 10^8 * 10^8.
To correctly use the Product Rule of Exponents, we need to multiply the bases and add the exponents when the bases are the same.
Let's look at the expressions one by one:
1. 6^2 * 7^3
In this expression, the bases are different (6 and 7), so we cannot directly apply the Product Rule. Therefore, this expression is not correctly developed to use the Product Rule.
2. (5^2)^9
In this expression, we have a base of 5 raised to the power of 2, and the whole expression is raised to the power of 9. To apply the Product Rule, we need to multiply the exponents. So, we have 2 * 9 = 18. The base remains the same, 5. Therefore, the expression correctly applies the Product Rule as 5^18.
3. 10^8 * 10^8
In this expression, we have the same base of 10 in both terms, which allows us to apply the Product Rule. We simply need to add the exponents, so we have 8 + 8 = 16. The base remains the same, 10. Therefore, the expression correctly applies the Product Rule as 10^16.
Out of the given options, the expression that is correctly developed to use the Product Rule of Exponents is:
2. (5^2)^9 = 5^18