Question
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(7 exponent8)⋅(7eponent10)
(7 exponent4)exponent8
(−5) exponent0
12 exponent9
👇
Responses
(7 exponent8)⋅(7eponent10)
(7 exponent4)exponent8
(−5) exponent0
12 exponent9
👇
Answers
GPT-4o mini
The Power Rule of Exponents states that when multiplying two exponents with the same base, you add the exponents, and when taking an exponent of an exponent, you multiply the exponents.
Let's examine the given expressions:
1. \( (7^{8}) \cdot (7^{10}) \) - This can be simplified using the Power Rule (add exponents) to get \( 7^{8+10} = 7^{18} \).
2. \( (7^{4})^{8} \) - This can be simplified using the Power Rule (multiply exponents) to get \( 7^{4 \cdot 8} = 7^{32} \).
3. \( (-5)^{0} \) - According to the Zero Exponent Rule, any non-zero number raised to the power of 0 equals 1. This expression does not require use of the Power Rule.
4. \( 12^{9} \) - This expression does not involve exponent rules but is simply a single exponent.
The expressions that can be correctly developed to use the Power Rule of Exponents are:
- \( (7^{8}) \cdot (7^{10}) \)
- \( (7^{4})^{8} \)
However, if we're looking for just one correct development based on the Power Rule, either option 1 or 2 would qualify, but option 1 is a straightforward application of the rule for multiplying exponents with the same base.
So, the best response to your question would be:
**(7 exponent8) ⋅ (7 exponent10)**
Let's examine the given expressions:
1. \( (7^{8}) \cdot (7^{10}) \) - This can be simplified using the Power Rule (add exponents) to get \( 7^{8+10} = 7^{18} \).
2. \( (7^{4})^{8} \) - This can be simplified using the Power Rule (multiply exponents) to get \( 7^{4 \cdot 8} = 7^{32} \).
3. \( (-5)^{0} \) - According to the Zero Exponent Rule, any non-zero number raised to the power of 0 equals 1. This expression does not require use of the Power Rule.
4. \( 12^{9} \) - This expression does not involve exponent rules but is simply a single exponent.
The expressions that can be correctly developed to use the Power Rule of Exponents are:
- \( (7^{8}) \cdot (7^{10}) \)
- \( (7^{4})^{8} \)
However, if we're looking for just one correct development based on the Power Rule, either option 1 or 2 would qualify, but option 1 is a straightforward application of the rule for multiplying exponents with the same base.
So, the best response to your question would be:
**(7 exponent8) ⋅ (7 exponent10)**
u sure ????????????
GPT-4o mini
Let's clarify a bit further to ensure we're on the same page regarding using the Power Rule of Exponents.
The Power Rule of Exponents states that:
1. When multiplying two expressions with the same base, you **add** the exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
2. When raising an exponent to another exponent, you **multiply** the exponents:
\[
(a^m)^n = a^{m \cdot n}
\]
Given the expressions you provided:
1. **(7 exponent8) ⋅ (7 exponent10)**: This can be simplified using the Power Rule by adding the exponents: \(7^{8 + 10} = 7^{18}\). **This uses the Power Rule.**
2. **(7 exponent4) exponent8**: This can be simplified by multiplying the exponents: \(7^{4 \cdot 8} = 7^{32}\). **This also uses the Power Rule.**
3. **(−5) exponent0**: According to the zero exponent rule, this equals 1, but it doesn't require the Power Rule for development. **This does not use the Power Rule.**
4. **12 exponent9**: This is just a single exponent with no operations on exponents. **This does not use the Power Rule.**
So to clarify, both the first expression **(7 exponent8) ⋅ (7 exponent10)** and the second expression **(7 exponent4) exponent8** are correctly developed to utilize the Power Rule of Exponents.
If you're asked to select one that clearly demonstrates the application of the Power Rule (specifically the multiplication of like bases), the first option is indeed a more straightforward illustration of that rule. However, both options 1 and 2 demonstrate exponent rules correctly.
If you are looking for just one clear correct answer focusing on multiplication of exponents, it is indeed:
**(7 exponent8) ⋅ (7 exponent10)**
I apologize for any confusion! Please let me know if you need further clarification.
The Power Rule of Exponents states that:
1. When multiplying two expressions with the same base, you **add** the exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
2. When raising an exponent to another exponent, you **multiply** the exponents:
\[
(a^m)^n = a^{m \cdot n}
\]
Given the expressions you provided:
1. **(7 exponent8) ⋅ (7 exponent10)**: This can be simplified using the Power Rule by adding the exponents: \(7^{8 + 10} = 7^{18}\). **This uses the Power Rule.**
2. **(7 exponent4) exponent8**: This can be simplified by multiplying the exponents: \(7^{4 \cdot 8} = 7^{32}\). **This also uses the Power Rule.**
3. **(−5) exponent0**: According to the zero exponent rule, this equals 1, but it doesn't require the Power Rule for development. **This does not use the Power Rule.**
4. **12 exponent9**: This is just a single exponent with no operations on exponents. **This does not use the Power Rule.**
So to clarify, both the first expression **(7 exponent8) ⋅ (7 exponent10)** and the second expression **(7 exponent4) exponent8** are correctly developed to utilize the Power Rule of Exponents.
If you're asked to select one that clearly demonstrates the application of the Power Rule (specifically the multiplication of like bases), the first option is indeed a more straightforward illustration of that rule. However, both options 1 and 2 demonstrate exponent rules correctly.
If you are looking for just one clear correct answer focusing on multiplication of exponents, it is indeed:
**(7 exponent8) ⋅ (7 exponent10)**
I apologize for any confusion! Please let me know if you need further clarification.
u sure ?????
GPT-4o mini
Yes, let’s break it down for absolute clarity:
To apply the **Power Rule of Exponents**, we focus on two main principles:
1. **Multiplying Exponents with the Same Base**:
\[
a^m \cdot a^n = a^{m+n}
\]
2. **Raising an Exponent to Another Exponent**:
\[
(a^m)^n = a^{m \cdot n}
\]
Now, looking at your expressions one last time:
1. **(7 exponent 8) ⋅ (7 exponent 10)**
- Here you are multiplying \(7^{8}\) by \(7^{10}\). According to the Power Rule, you can add the exponents:
\[
7^{8} \cdot 7^{10} = 7^{8 + 10} = 7^{18}
\]
**This correctly applies the Power Rule.**
2. **(7 exponent 4) exponent 8**
- Here you are raising \(7^{4}\) to the power of 8. Using the Power Rule, you can multiply the exponents:
\[
(7^{4})^{8} = 7^{4 \cdot 8} = 7^{32}
\]
**This also correctly applies the Power Rule.**
3. **(−5) exponent 0**
- According to the zero exponent rule, any non-zero number raised to the power of 0 is 1. This does not involve any multiplication or raising of exponents.
**This does not use the Power Rule.**
4. **12 exponent 9**
- This is simply \(12^{9}\) with no operations involving exponents. There’s no application of the Power Rule here.
**This does not use the Power Rule.**
So, number 1 and number 2 both demonstrate correct applications of the Power Rule. However, if you have to choose just one example that highlights the multiplication of exponents, then **(7 exponent 8) ⋅ (7 exponent 10)** would be the most straightforward and clear example.
If this is still not what you were questioning, please let me know, and I’d be happy to clarify further!
To apply the **Power Rule of Exponents**, we focus on two main principles:
1. **Multiplying Exponents with the Same Base**:
\[
a^m \cdot a^n = a^{m+n}
\]
2. **Raising an Exponent to Another Exponent**:
\[
(a^m)^n = a^{m \cdot n}
\]
Now, looking at your expressions one last time:
1. **(7 exponent 8) ⋅ (7 exponent 10)**
- Here you are multiplying \(7^{8}\) by \(7^{10}\). According to the Power Rule, you can add the exponents:
\[
7^{8} \cdot 7^{10} = 7^{8 + 10} = 7^{18}
\]
**This correctly applies the Power Rule.**
2. **(7 exponent 4) exponent 8**
- Here you are raising \(7^{4}\) to the power of 8. Using the Power Rule, you can multiply the exponents:
\[
(7^{4})^{8} = 7^{4 \cdot 8} = 7^{32}
\]
**This also correctly applies the Power Rule.**
3. **(−5) exponent 0**
- According to the zero exponent rule, any non-zero number raised to the power of 0 is 1. This does not involve any multiplication or raising of exponents.
**This does not use the Power Rule.**
4. **12 exponent 9**
- This is simply \(12^{9}\) with no operations involving exponents. There’s no application of the Power Rule here.
**This does not use the Power Rule.**
So, number 1 and number 2 both demonstrate correct applications of the Power Rule. However, if you have to choose just one example that highlights the multiplication of exponents, then **(7 exponent 8) ⋅ (7 exponent 10)** would be the most straightforward and clear example.
If this is still not what you were questioning, please let me know, and I’d be happy to clarify further!