Which expression is correctly developed to use the product rule of exponents?
1. 10^8 * 10^8
2. (5^2)^9
3. 32^7
4. 6^ * 7^3
The correct expression that uses the product rule of exponents is:
1. 10^8 * 10^8
The expression that is correctly developed to use the product rule of exponents is 1. 10^8 * 10^8.
To correctly apply the product rule of exponents, we need to multiply exponential expressions with the same base. The product rule states that when multiplying two exponential expressions with the same base, we add their exponents.
Let's look at the options:
1. 10^8 * 10^8
This option follows the product rule because the base (10) is the same in both exponentials. To calculate the result, we add the exponents together: 8 + 8 = 16. Therefore, 10^8 * 10^8 is equal to 10^16.
2. (5^2)^9
In this case, we have an exponential expression inside parentheses. To apply the product rule, we consider the exponent outside the parentheses (9) and multiply it by the exponent inside the parentheses (2). Therefore, (5^2)^9 simplifies to 5^(2 * 9) = 5^18.
3. 32^7
This expression does not involve the product rule because there is only one exponential expression present. Therefore, we do not need to apply the product rule in this case.
4. 6^ * 7^3
This expression is incomplete as it lacks an exponent for the base 6. To properly apply the product rule, a complete exponential expression with exponents for both bases is required.
In summary, the expression that correctly utilizes the product rule of exponents is option 1: 10^8 * 10^8.