The expression that is correctly developed to use the Product Rule of Exponents is:
(52)9
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
62⋅73
6 squared times 7 cubed
10 superscript 8 baseline times 10 superscript 8 baseline
327
32 superscript 7 baseline
(52)9
5 answers
wrong
Apologies for the incorrect response. The correct expression that is correctly developed to use the Product Rule of Exponents is:
10⁸ * 10⁸
10⁸ * 10⁸
can you explain
Certainly!
The Product Rule of Exponents states that when you multiply two exponential expressions with the same base, you add their exponents. In other words, for any number x and any exponents a and b, if you have x^a * x^b, you can simplify it to x^(a + b).
Let's apply this rule to the expression 6^2 * 7^3:
1. 6^2 represents 6 raised to the power of 2, which means you multiply 6 by itself: 6^2 = 6 * 6 = 36.
2. 7^3 represents 7 raised to the power of 3, which means you multiply 7 by itself two more times: 7^3 = 7 * 7 * 7 = 343.
Now, using the Product Rule, we can multiply these two exponential expressions: 6^2 * 7^3 = 36 * 343.
Since the base is the same (6 and 7), we add the exponents: 2 + 3 = 5.
So, 6^2 * 7^3 can be simplfied to 36 * 343, which equals 12,288.
I hope this explanation helps! Let me know if you have any further questions.
The Product Rule of Exponents states that when you multiply two exponential expressions with the same base, you add their exponents. In other words, for any number x and any exponents a and b, if you have x^a * x^b, you can simplify it to x^(a + b).
Let's apply this rule to the expression 6^2 * 7^3:
1. 6^2 represents 6 raised to the power of 2, which means you multiply 6 by itself: 6^2 = 6 * 6 = 36.
2. 7^3 represents 7 raised to the power of 3, which means you multiply 7 by itself two more times: 7^3 = 7 * 7 * 7 = 343.
Now, using the Product Rule, we can multiply these two exponential expressions: 6^2 * 7^3 = 36 * 343.
Since the base is the same (6 and 7), we add the exponents: 2 + 3 = 5.
So, 6^2 * 7^3 can be simplfied to 36 * 343, which equals 12,288.
I hope this explanation helps! Let me know if you have any further questions.