Which expression is correctly developed to use the product rule of exponents?
10 8 .10 8
32 7
(5 2,)9
6 2 .7 3
(10^8)(10^8)
To use the product rule of exponents, we need to multiply the exponential expressions together.
Let's go through each option:
1) 10^8.10^8
This expression is incorrect. To multiply exponential expressions, we add the exponents. The correct expression would be (10^8)(10^8) = 10^(8+8) = 10^16.
2) 32^7
This expression is already in the correct form. There is no need to use the product rule of exponents.
3) (5^2)^9
This expression is also already in the correct form. Again, there is no need to use the product rule of exponents.
4) 6^2.7^3
This expression can be simplified using the product rule of exponents. The rule states that when multiplying exponential expressions with the same base, we add the exponents.
So, 6^2.7^3 = 6^(2+3) = 6^5.
Therefore, the expression that is correctly developed to use the product rule of exponents is 6^2.7^3 = 6^5.
To correctly apply the product rule of exponents, we need to remember the rule:
a^m * a^n = a^(m+n)
Let's examine each expression and determine if it follows this rule:
1. 10^8 * 10^8:
We can rewrite this expression using the product rule of exponents. Since the bases are the same (10), we add the exponents: 8 + 8 = 16. Therefore, the correct expression is 10^16.
2. 32^7:
This expression does not involve the product rule of exponents. It is simply raising 32 to the power of 7. So, the expression remains as 32^7.
3. (5^2)^9:
This expression simplifies using the product rule of exponents. To apply the rule, we need to multiply the exponents: 2 * 9 = 18. Therefore, the correct expression is 5^18.
4. 6^2 * 7^3:
Here, we have two bases (6 and 7), and the exponents cannot be combined as they're associated with different bases. Therefore, the expression remains as 6^2 * 7^3.
To summarize, using the product rule of exponents:
1. 10^8 * 10^8 = 10^16
2. 32^7 remains as 32^7
3. (5^2)^9 = 5^18
4. 6^2 * 7^3 remains as 6^2 * 7^3