Question
1. What is the Quotient Rule of Integer Exponents?(1 point)%0D%0AResponses%0D%0A%0D%0Axaxb=xa+b%0D%0Aπ₯%0D%0Aπ%0D%0Aπ₯%0D%0Aπ%0D%0A=%0D%0Aπ₯%0D%0Aπ%0D%0A+%0D%0Aπ%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A plus b power%0D%0A%0D%0Axaxb=xaβb%0D%0Aπ₯%0D%0Aπ%0D%0Aπ₯%0D%0Aπ%0D%0A=%0D%0Aπ₯%0D%0Aπ%0D%0Aβ%0D%0Aπ%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A minus b power%0D%0A%0D%0Axaxb=xab%0D%0Aπ₯%0D%0Aπ%0D%0Aπ₯%0D%0Aπ%0D%0A=%0D%0Aπ₯%0D%0Aπ%0D%0Aπ%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A b power%0D%0A%0D%0Axaxb=xbβa
2. Simplify x675/x453%0D%0Aπ₯%0D%0A675%0D%0Aπ₯%0D%0A453%0D%0A.(1 point)
3. What is the missing exponent in the following equation?%0D%0Ae^?/e^65 = e^38%0D%0Aπ%0D%0A?%0D%0Aπ%0D%0A65%0D%0A %0D%0A=%0D%0A %0D%0Aπ%0D%0A38%0D%0A(1 point)
4. Simplify 13^12Γ·13^β10
5. Simplify 4^13Γ·3^β5%0D%0A4%0D%0A13%0D%0AΓ·%0D%0A3%0D%0Aβ%0D%0A5%0D%0A .
2. Simplify x675/x453%0D%0Aπ₯%0D%0A675%0D%0Aπ₯%0D%0A453%0D%0A.(1 point)
3. What is the missing exponent in the following equation?%0D%0Ae^?/e^65 = e^38%0D%0Aπ%0D%0A?%0D%0Aπ%0D%0A65%0D%0A %0D%0A=%0D%0A %0D%0Aπ%0D%0A38%0D%0A(1 point)
4. Simplify 13^12Γ·13^β10
5. Simplify 4^13Γ·3^β5%0D%0A4%0D%0A13%0D%0AΓ·%0D%0A3%0D%0Aβ%0D%0A5%0D%0A .
Answers
Answer
tell me what to put for the answers
Answer
1. x^a/x^b = x^a-b
2. x^222
3. 103
4. 13^22
5. 4^13 divide symbol 3^-5
2. x^222
3. 103
4. 13^22
5. 4^13 divide symbol 3^-5
Answer
1. Simplify this expression using the Quotient Rule of Integer Exponents: t400/t100.
t^300, 300, t^4, t^500
2.Simplify a67/b34.(1 point)%0D%0AResponses%0D%0A%0D%0Aab33%0D%0Aa b superscript 33 baseline%0D%0A%0D%0A23%0D%0A23%0D%0A%0D%0Aa67b34%0D%0AStart Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction%0D%0A%0D%0Aa33
3. Apply the Quotient Rule of Integer Exponents to simplify 23^65Γ·23^32.
97, 23^33, 1^33, 23^97
4. Simplify this expression using the Quotient Rule of Integer Exponents: 12^53Γ·7^53.
12^53 divided symbol 7^53, 5^53, 12^106, 5^106
5. Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)%0D%0AResponses%0D%0A%0D%0ACheck if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.%0D%0ACheck if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.%0D%0A%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ACheck if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
say the answers
t^300, 300, t^4, t^500
2.Simplify a67/b34.(1 point)%0D%0AResponses%0D%0A%0D%0Aab33%0D%0Aa b superscript 33 baseline%0D%0A%0D%0A23%0D%0A23%0D%0A%0D%0Aa67b34%0D%0AStart Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction%0D%0A%0D%0Aa33
3. Apply the Quotient Rule of Integer Exponents to simplify 23^65Γ·23^32.
97, 23^33, 1^33, 23^97
4. Simplify this expression using the Quotient Rule of Integer Exponents: 12^53Γ·7^53.
12^53 divided symbol 7^53, 5^53, 12^106, 5^106
5. Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)%0D%0AResponses%0D%0A%0D%0ACheck if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.%0D%0ACheck if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.%0D%0A%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ACheck if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
say the answers
Answer
1. t^300
2. a^67/b^34
3. 23^33
4. 12^53 divide symbol 7^53
5. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
2. a^67/b^34
3. 23^33
4. 12^53 divide symbol 7^53
5. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Answered by
GPT-4o mini
1. **Quotient Rule of Integer Exponents**: The Quotient Rule states that for any nonzero base \( x \) and integers \( a \) and \( b \),
\[
\frac{x^a}{x^b} = x^{a - b}.
\]
(This means that when you divide powers with the same base, you subtract the exponents.)
2. **Simplify \( \frac{x^{675}}{x^{453}} \)**:
Using the Quotient Rule,
\[
\frac{x^{675}}{x^{453}} = x^{675 - 453} = x^{222}.
\]
3. **Find the missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \)**:
According to the Quotient Rule,
\[
e^{? - 65} = e^{38}.
\]
Setting the exponents equal to each other gives:
\[
? - 65 = 38.
\]
Solving for \( ? \):
\[
? = 38 + 65 = 103.
\]
4. **Simplify \( 13^{12} \div 13^{-10} \)**:
Using the Quotient Rule,
\[
13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}.
\]
5. **Simplify \( 4^{13} \div 3^{-5} \)**:
For this expression, since \( 3^{-5} \) is in the denominator, we can rewrite it as:
\[
4^{13} \div 3^{-5} = 4^{13} \cdot 3^{5} = 4^{13} \cdot 3^5.
\]
So the final expression is:
\[
4^{13} \cdot 3^{5}.
\]
\[
\frac{x^a}{x^b} = x^{a - b}.
\]
(This means that when you divide powers with the same base, you subtract the exponents.)
2. **Simplify \( \frac{x^{675}}{x^{453}} \)**:
Using the Quotient Rule,
\[
\frac{x^{675}}{x^{453}} = x^{675 - 453} = x^{222}.
\]
3. **Find the missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \)**:
According to the Quotient Rule,
\[
e^{? - 65} = e^{38}.
\]
Setting the exponents equal to each other gives:
\[
? - 65 = 38.
\]
Solving for \( ? \):
\[
? = 38 + 65 = 103.
\]
4. **Simplify \( 13^{12} \div 13^{-10} \)**:
Using the Quotient Rule,
\[
13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}.
\]
5. **Simplify \( 4^{13} \div 3^{-5} \)**:
For this expression, since \( 3^{-5} \) is in the denominator, we can rewrite it as:
\[
4^{13} \div 3^{-5} = 4^{13} \cdot 3^{5} = 4^{13} \cdot 3^5.
\]
So the final expression is:
\[
4^{13} \cdot 3^{5}.
\]
Answered by
GPT-4o mini
Sure! Here are the answers you can submit for each question:
1. **Quotient Rule of Integer Exponents:**
\( \frac{x^a}{x^b} = x^{a - b} \)
2. **Simplify \( \frac{x^{675}}{x^{453}} \):**
\( x^{222} \)
3. **Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):**
\( 103 \)
4. **Simplify \( 13^{12} \div 13^{-10} \):**
\( 13^{22} \)
5. **Simplify \( 4^{13} \div 3^{-5} \):**
\( 4^{13} \cdot 3^{5} \)
Feel free to ask if you need any further assistance!
1. **Quotient Rule of Integer Exponents:**
\( \frac{x^a}{x^b} = x^{a - b} \)
2. **Simplify \( \frac{x^{675}}{x^{453}} \):**
\( x^{222} \)
3. **Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):**
\( 103 \)
4. **Simplify \( 13^{12} \div 13^{-10} \):**
\( 13^{22} \)
5. **Simplify \( 4^{13} \div 3^{-5} \):**
\( 4^{13} \cdot 3^{5} \)
Feel free to ask if you need any further assistance!
Answered by
GPT-4o mini
Your answers look mostly correct! However, there is a small adjustment needed for the format of the last answer. Here's a recap of your answers along with the suggested fix for question 5:
1. **Quotient Rule of Integer Exponents:**
\( \frac{x^a}{x^b} = x^{a - b} \) (correct)
2. **Simplify \( \frac{x^{675}}{x^{453}} \):**
\( x^{222} \) (correct)
3. **Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):**
\( 103 \) (correct)
4. **Simplify \( 13^{12} \div 13^{-10} \):**
\( 13^{22} \) (correct)
5. **Simplify \( 4^{13} \div 3^{-5} \):**
Instead of writing "divide symbol", you can write it as:
\( 4^{13} \cdot 3^{5} \) (because dividing by \( 3^{-5} \) is the same as multiplying by \( 3^{5} \)).
So the responses would look like this:
1. \( \frac{x^a}{x^b} = x^{a - b} \)
2. \( x^{222} \)
3. \( 103 \)
4. \( 13^{22} \)
5. \( 4^{13} \cdot 3^{5} \)
Feel free to submit these! If you need any more help, let me know!
1. **Quotient Rule of Integer Exponents:**
\( \frac{x^a}{x^b} = x^{a - b} \) (correct)
2. **Simplify \( \frac{x^{675}}{x^{453}} \):**
\( x^{222} \) (correct)
3. **Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):**
\( 103 \) (correct)
4. **Simplify \( 13^{12} \div 13^{-10} \):**
\( 13^{22} \) (correct)
5. **Simplify \( 4^{13} \div 3^{-5} \):**
Instead of writing "divide symbol", you can write it as:
\( 4^{13} \cdot 3^{5} \) (because dividing by \( 3^{-5} \) is the same as multiplying by \( 3^{5} \)).
So the responses would look like this:
1. \( \frac{x^a}{x^b} = x^{a - b} \)
2. \( x^{222} \)
3. \( 103 \)
4. \( 13^{22} \)
5. \( 4^{13} \cdot 3^{5} \)
Feel free to submit these! If you need any more help, let me know!
Answered by
GPT-4o mini
Here are the answers for each of the questions you provided:
1. **Simplify \( \frac{t^{400}}{t^{100}} \):**
Using the Quotient Rule:
\[
\frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}.
\]
**Answer:** \( t^{300} \)
2. **Simplify \( \frac{a^{67}}{b^{34}} \):**
This expression cannot be simplified by the Quotient Rule, as the bases \( a \) and \( b \) are different. The expression remains as \( \frac{a^{67}}{b^{34}} \) but you have the option of \( a^{33} \) if you are focusing on common exponent factorization of \( a \):
\[
\text{Answer: } a^{67} b^{-34} \text{ (which can be expressed as } a^{67} \text{ and } b^{-34} \text{: not applicable for direct simplification)}.
\]
**Answer:** \( a^{67} b^{-34} \) (if applicable based on your response options).
3. **Simplify \( 23^{65} \div 23^{32} \):**
Using the Quotient Rule:
\[
23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33}.
\]
**Answer:** \( 23^{33} \)
4. **Simplify \( \frac{12^{53}}{7^{53}} \):**
Since the bases are different, we apply the Quotient Rule:
\[
\frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53}.
\]
However, this is not an option provided. If simply looking for the expression \( \frac{12^{53}}{7^{53}} \):
**Answer:** \( \frac{12^{53}}{7^{53}} \) (can also express as \( \left( \frac{12}{7} \right)^{53} \) if needed).
5. **Correct steps to simplify an exponential expression using the Quotient Rule:**
**Answer:**
\( \text{Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.} \)
Feel free to ask if you need more clarification or additional assistance!
1. **Simplify \( \frac{t^{400}}{t^{100}} \):**
Using the Quotient Rule:
\[
\frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}.
\]
**Answer:** \( t^{300} \)
2. **Simplify \( \frac{a^{67}}{b^{34}} \):**
This expression cannot be simplified by the Quotient Rule, as the bases \( a \) and \( b \) are different. The expression remains as \( \frac{a^{67}}{b^{34}} \) but you have the option of \( a^{33} \) if you are focusing on common exponent factorization of \( a \):
\[
\text{Answer: } a^{67} b^{-34} \text{ (which can be expressed as } a^{67} \text{ and } b^{-34} \text{: not applicable for direct simplification)}.
\]
**Answer:** \( a^{67} b^{-34} \) (if applicable based on your response options).
3. **Simplify \( 23^{65} \div 23^{32} \):**
Using the Quotient Rule:
\[
23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33}.
\]
**Answer:** \( 23^{33} \)
4. **Simplify \( \frac{12^{53}}{7^{53}} \):**
Since the bases are different, we apply the Quotient Rule:
\[
\frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53}.
\]
However, this is not an option provided. If simply looking for the expression \( \frac{12^{53}}{7^{53}} \):
**Answer:** \( \frac{12^{53}}{7^{53}} \) (can also express as \( \left( \frac{12}{7} \right)^{53} \) if needed).
5. **Correct steps to simplify an exponential expression using the Quotient Rule:**
**Answer:**
\( \text{Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.} \)
Feel free to ask if you need more clarification or additional assistance!
Answered by
GPT-4o mini
Your answers look great! Hereβs a final recap to confirm:
1. **Simplified expression for** \( \frac{t^{400}}{t^{100}} \):
**Answer:** \( t^{300} \)
2. **Simplified expression for** \( \frac{a^{67}}{b^{34}} \):
**Answer:** \( \frac{a^{67}}{b^{34}} \) (or \( a^{67}b^{-34} \) if transformed)
3. **Simplified expression for** \( 23^{65} \div 23^{32} \):
**Answer:** \( 23^{33} \)
4. **Simplified expression for** \( \frac{12^{53}}{7^{53}} \):
**Answer:** \( \frac{12^{53}}{7^{53}} \) (or as \( (12/7)^{53} \) if needed)
5. **Steps to simplify an exponential expression using the Quotient Rule:**
**Answer:**
**Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.**
You have provided the correct answers based on the questions! If you have any further questions or need assistance, feel free to ask!
1. **Simplified expression for** \( \frac{t^{400}}{t^{100}} \):
**Answer:** \( t^{300} \)
2. **Simplified expression for** \( \frac{a^{67}}{b^{34}} \):
**Answer:** \( \frac{a^{67}}{b^{34}} \) (or \( a^{67}b^{-34} \) if transformed)
3. **Simplified expression for** \( 23^{65} \div 23^{32} \):
**Answer:** \( 23^{33} \)
4. **Simplified expression for** \( \frac{12^{53}}{7^{53}} \):
**Answer:** \( \frac{12^{53}}{7^{53}} \) (or as \( (12/7)^{53} \) if needed)
5. **Steps to simplify an exponential expression using the Quotient Rule:**
**Answer:**
**Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.**
You have provided the correct answers based on the questions! If you have any further questions or need assistance, feel free to ask!
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