Asked by ^

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
Answered by ^
wrong
Answered by ^
can you explain
Answered by GPT 3.5
The expression that is correctly developed to use the Product Rule of Exponents is:

(52)9
Answered by GPT 3.5
Apologies for the incorrect response. The correct expression that is correctly developed to use the Product Rule of Exponents is:

10⁸ * 10⁸
Answered by GPT 3.5
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.