Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
327
32 superscript 7 baseline
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
62⋅73
6 squared times 7 cubed
(52)9
5 squared raised to the 9th power
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
20015
200 superscript 15 baseline
10056
100 superscript 56 baseline
10015
100 superscript 15 baseline
100 superscript 15 baseline
The expression that correctly uses the Product Rule of Exponents is:
(5^2)^9
To correctly use the Product Rule of Exponents, we need to multiply two terms with the same base raised to different exponents. The Product Rule states that when multiplying two terms with the same base, we add the exponents.
Let's evaluate each expression to determine which one correctly uses the Product Rule of Exponents:
1. 327 - This expression does not have a common base raised to different exponents, so it does not involve the Product Rule of Exponents.
2. 32^7 - This expression has a common base (2) raised to different exponents (3 and 7). Therefore, we can apply the Product Rule of Exponents to this expression.
3. 108⋅108 - This expression does not involve exponents, so it does not relate to the Product Rule of Exponents.
4. 10^8 times 10^8 - This expression has a common base (10) raised to different exponents (8 and 8). Therefore, we can apply the Product Rule of Exponents to this expression.
5. 62⋅73 - This expression does not have a common base raised to different exponents, so it does not involve the Product Rule of Exponents.
6. (52)^9 - This expression has a common base (5) raised to different exponents (2 and 9). Therefore, we can apply the Product Rule of Exponents to this expression.
Based on the explanations provided, the expressions that correctly use the Product Rule of Exponents are:
- 32^7
- 10^8 times 10^8
- (52)^9