Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
327
32 superscript 7 baseline
(52)9
left parenthesis 5 squared right parenthesis superscript 9 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
10,00015
10,000 superscript 15 baseline
10056
100 superscript 56 baseline
10015
100 superscript 15 baseline
20015
200 superscript 15 baseline
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
100,000
100,000
1,100
1,100
10
10
105
1,000
The expression that is correctly developed to use the Product Rule of Exponents is:
6^2 * 7^3
To correctly use the Product Rule of Exponents, we need to multiply two numbers with the same base raised to different exponents. The Product Rule states that when multiplying expressions with the same base, you can add the exponents together.
Let's examine the options provided:
1. 108⋅108: This expression does not involve the same base raised to different exponents. The base is 10 and the exponents are both 8, which means it can't utilize the Product Rule of Exponents.
2. 10^8 times 10^8: This expression correctly utilizes the Product Rule of Exponents. The base is 10, and the exponents are both 8. According to the Product Rule, we can add the exponents, resulting in 10^(8+8) = 10^16.
3. 32^7: This expression does not involve the same base raised to different exponents. The base is 32, and the exponent is 7, so it cannot use the Product Rule.
4. (52)^9: This expression also does not involve the same base raised to different exponents. The base is 52, and the exponent is 9, so it doesn't follow the Product Rule.
Therefore, the correct expression that uses the Product Rule of Exponents is 10^8 times 10^8, which simplifies to 10^16.