Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
A.10^(8) * 10^(8)
B.32^(7)
C.(5^(2))^(9)
D.6^(2) * 7^(3)
D.6^(2) * 7^(3)
The Product Rule of Exponents states that when you multiply two numbers with the same base, you can add their exponents.
Let's go through the options one by one:
A. 10^(8) * 10^(8)
This expression is the product of two numbers with the same base (10), so we can add their exponents:
10^(8 + 8) = 10^(16)
B. 32^(7)
This expression does not involve multiplying two numbers with the same base, so the Product Rule of Exponents does not apply here.
C. (5^(2))^(9)
This expression represents raising a number to a power and then raising the result to another power. To simplify this, we multiply the exponents:
(5^(2))^(9) = 5^(2 * 9) = 5^(18)
D. 6^(2) * 7^(3)
This expression involves multiplying two numbers with different bases (6 and 7), so the Product Rule of Exponents does not apply here.
Therefore, the expression that is correctly developed to use the Product Rule of Exponents is A.10^(8) * 10^(8) = 10^(16).
The Product Rule of Exponents states that when multiplying two numbers with the same base, you can add their exponents. To determine which expression correctly uses the Product Rule of Exponents, we need to identify the expressions that involve multiplication with the same base.
Let's analyze the options one by one:
A. 10^(8) * 10^(8)
This expression involves multiplication with the same base, which is 10. The exponents are both 8. Therefore, this expression correctly uses the Product Rule of Exponents.
B. 32^(7)
This expression does not involve multiplication with the same base. It only has one base, which is 32. Therefore, this expression does not use the Product Rule of Exponents.
C. (5^(2))^(9)
This expression involves exponentiation, but it does not involve multiplication with the same base. The base is 5 to the power of 2, and the exponent is 9. Therefore, this expression does not use the Product Rule of Exponents.
D. 6^(2) * 7^(3)
This expression involves multiplication with different bases, which are 6 and 7. Therefore, this expression does not use the Product Rule of Exponents.
Therefore, the correct expression that uses the Product Rule of Exponents is A. 10^(8) * 10^(8).