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
The expression that is correctly developed to use the Product Rule of Exponents is:
(52)9
The expression that is correctly developed to use the Product Rule of Exponents is:
(6²) * (7³)
wrong
Apologies for the incorrect response. The correct expression that is correctly developed to use the Product Rule of Exponents is:
10⁸ * 10⁸
The expression that correctly uses the Product Rule of Exponents is "6 squared times 7 cubed" or 62⋅73.
To understand why it follows the Product Rule, let's review the rule itself. The Product Rule states that when multiplying two exponential expressions with the same base, you add their exponents. In other words, for a and b as exponents and x as the base, if you have x^a * x^b, you can simplify it to x^(a + b).
Now, let's look at the options:
1. 62⋅73: This expression represents 6 raised to the power of 2 multiplied by 7 raised to the power of 3. It follows the Product Rule because both exponents are added: 2 + 3 = 5. So, this expression correctly applies the Product Rule.
2. 10^8 * 10^8: This expression represents 10 raised to the power of 8 multiplied by 10 raised to the power of 8. The exponents are the same, so we can add them: 8 + 8 = 16. So, this expression also correctly applies the Product Rule.
3. 32^7: This expression represents 32 raised to the power of 7. There is no multiplication involved here, so it does not utilize the Product Rule.
4. (52)^9: This expression represents 52 raised to the power of 9. It also does not involve multiplication, so it does not utilize the Product Rule.
In conclusion, the expression that correctly utilizes the Product Rule of Exponents is "6 squared times 7 cubed" or 62⋅73.
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.