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
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
108⋅108
1 squared times 8 squared
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
32^7
6^7x7^3
(5^)^9
10^8x10^8
6^2 * 7^3
Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8x100^7?
The expression that correctly used the Product Rule of Exponents to simplify the expression 100^8x100^7 is:
(100^8) * (100^7)
The correct expression to use the Product Rule of Exponents is (52)9.
To apply the Product Rule of Exponents, we need to multiply two expressions with the same base raised to different exponents. The Product Rule states that when multiplying two expressions with the same base, we can add their exponents.
Let's analyze the options:
1. 327: This does not involve any exponents, so it does not apply the Product Rule of Exponents.
2. 32^7: Here we have a base of 3 raised to the exponent of 2. This would be correct if the exponent were 7, not 2. Therefore, it does not follow the Product Rule.
3. 62⋅73: In this expression, we have a base of 6 raised to the exponent of 2, and a base of 7 raised to the exponent of 3. This correctly applies the Product Rule of exponents since we are multiplying two expressions with the same base but different exponents. The answer is 6^2 * 7^3.
4. (52)9: Here we have a base of 5 raised to the exponent of 2, taken to the exponent of 9. This does not follow the Product Rule of Exponents since we are not multiplying two expressions with the same base but different exponents.
5. 108⋅108: This does not involve any exponents, so it does not apply the Product Rule of Exponents.
Therefore, the expression that correctly applies the Product Rule of Exponents is 62⋅73 (Option 3) which is equal to 6^2 * 7^3.