Answer:
(5³)⁹ and 10⁸ . 10⁸
Explanation:
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add their exponents.
Let's examine each expression to see which one correctly uses the Product Rule of Exponents:
a. 6³ . 7³: This expression has two numbers with the same base, 6 and 7. However, the exponents are not added together. Therefore, this expression does not use the Product Rule of Exponents.
b. (5³)⁹: This expression has a number, 5, raised to a power of 3, and then the result is raised to a power of 9. To apply the Product Rule of Exponents, we need to multiply the exponents. Since 3 multiplied by 9 equals 27, this expression correctly uses the Product Rule of Exponents.
c. 10⁸ . 10⁸: This expression has two numbers with the same base, 10. The exponents are both 8, and to multiply the numbers, we add the exponents. Therefore, this expression correctly uses the Product Rule of Exponents.
d. 32⁷: This expression only has one number, 32, raised to the power of 7. There is no other number with the same base to apply the Product Rule of Exponents. Therefore, this expression does not use the Product Rule of Exponents.
In conclusion, the expressions that correctly use the Product Rule of Exponents are (5³)⁹ and 10⁸ . 10⁸, which are options b and c, respectively.