Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
327
32 superscript 7 baseline
62⋅73
6 superscript 2 baseline times 7 superscript 3 baseline
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10056
100 superscript 56 baseline
10,00015
10,000 superscript 15 baseline
10015
100 superscript 15 baseline
20015
10,000 superscript 15 baseline
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
105
10 superscript 5 baseline
10
10
100,000
100,000
1,100
1,100
Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses
128
128
2
2
8
8
16
8
Find the numerical equivalent of 49⋅4−7(1 point)
Responses
42
4 squared
4
4
416
4 superscript 16 baseline
16
16
To use the Product Rule of Exponents, the rule states that when multiplying two exponential terms with the same base, you can add their exponents together.
Let's analyze the given options:
Option 1: (52)9
In this option, the base is 5 and the exponent is 2. However, there is no multiplication happening, so the Product Rule of Exponents is not applicable here.
Option 2: 108⋅108
In this option, we have two terms, both with a base of 10. The exponents are both 8. Since we are multiplying these terms, we can apply the Product Rule of Exponents by adding the exponents together. Hence, this option correctly utilizes the Product Rule of Exponents.
Option 3: 327
In this option, we only have a single term with a base of 32 and an exponent of 7. There is no multiplication, so the Product Rule of Exponents does not apply here.
Option 4: 62⋅73
This option involves the multiplication of two terms with different bases. The Product Rule of Exponents only applies when the bases are the same. Therefore, this option does not correctly use the Product Rule of Exponents.
Based on our analysis, option 2 is the correct expression that uses the Product Rule of Exponents correctly.