Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
62⋅73
6 squared times 7 cubed
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
327
32 superscript 7 baseline
108⋅108
10 squared times 10 squared
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10,00015
10,000 superscript 15 baseline
10056
100 superscript 56 baseline
10015
100 superscript 15 baseline
20015
None of the given responses correctly use the Product Rule of Exponents to simplify the expression 1008⋅1007.
To use the product rule of exponents, you multiply the base numbers and add the exponents.
The correct expression that uses the product rule of exponents is:
(6^2) * (7^3)
To correctly apply the Product Rule of Exponents, we need to multiply the bases and add the exponents. The Product Rule states that when you multiply two numbers with the same base, you add their exponents.
Let's analyze the given expressions:
1. 62⋅73:
To use the Product Rule of Exponents in this expression, we need to consider the bases and exponents separately. The base for both numbers is 6, and the exponents are 2 and 3. We multiply the bases (6 times 7) and add the exponents (2 plus 3) to get 6 squared times 7 cubed.
2. (52)9:
In this expression, the base is 5, and the exponent is 2. However, the exponent is enclosed in parentheses and multiplied by 9. To simplify this expression, we need to apply the exponent first and then multiply by 9. So, we calculate 5 squared, which is 25, and then multiply it by 9.
3. 327:
This expression does not involve any exponents or bases that can be simplified using the Product Rule of Exponents. It is simply the number 327.
4. 108⋅108:
Just like the first expression, we have two numbers with the same base, which is 10, and an exponent of 8 for both. To apply the Product Rule of Exponents, we multiply the bases (10 times 10) and add the exponents (8 plus 8).
Therefore, the expression that correctly uses the Product Rule is 108⋅108.