Which expression is correctly developed to use the Product Rule of Exponents?(1 point) Responses 327 32 superscript 7 baseline 62⋅73 6 squared times 7 cubed 108⋅108 10 superscript 8 baseline times 10 superscript 8 baseline (52)9 left parenthesis 5 squared right parenthesis superscript 9 baseline
(5^2)^9
The correct expression that uses the Product Rule of Exponents is:
(5^2)^9
To use the Product Rule of Exponents, we can multiply two terms with the same base and different exponents. The rule states that if we have the same base raised to different powers, we can keep the base and add the exponents together.
Let's look at the given expressions:
1. 327: This expression does not have the same base raised to different exponents, so it does not involve the Product Rule of Exponents.
2. 32^7: Here, we have the base 3 raised to two different exponents, 2 and 7. To apply the Product Rule, we keep the base and add the exponents together. Therefore, the correct development would be 3^(2+7) = 3^9.
3. 62⋅73: This expression is a multiplication of two terms, but they have different bases. It does not involve the Product Rule of Exponents.
4. 6^2 times 7^3: In this expression, we have the bases 6 and 7 raised to different exponents, 2 and 3, respectively. To apply the Product Rule, we keep the bases and add the exponents together. The correct development would be 6^2 * 7^3.
5. 108⋅108: This expression involves a multiplication of two terms, but they have the same base raised to the same exponent. It does not involve the Product Rule of Exponents.
6. 10^8 times 10^8: Here, we have the base 10 raised to the same exponent, 8, in both terms. To apply the Product Rule, we keep the base and add the exponents together. The correct development would be 10^(8+8) = 10^16.
7. (52)^9: This expression has a base inside parentheses raised to an exponent. It does not involve the Product Rule of Exponents.
Therefore, the correct expression that uses the Product Rule of Exponents is "6^2 times 7^3".