Question
Simplify this expression using the Quotient Rule of Integer Exponents: t400t100.(1 point)
Responses
t4
t superscript 4 baseline
t300
t superscript 300 baseline
300
300
t500
Responses
t4
t superscript 4 baseline
t300
t superscript 300 baseline
300
300
t500
Answers
Answer
Simplify a67b34.(1 point)
Responses
23
23
a33
a superscript 33 baseline
a67b34
Start Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction
ab33
Responses
23
23
a33
a superscript 33 baseline
a67b34
Start Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction
ab33
Answer
Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332 .(1 point)
Responses
97
97
2397
23 superscript 97 baseline
2333
23 superscript 33 baseline
133
Responses
97
97
2397
23 superscript 97 baseline
2333
23 superscript 33 baseline
133
Answer
Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753.(1 point)
Responses
5106
5 superscript 106 baseline
553
5 superscript 53 baseline
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
Responses
5106
5 superscript 106 baseline
553
5 superscript 53 baseline
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
12106
Answer
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
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.
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.
Check 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.
Check 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.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Responses
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.
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.
Check 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.
Check 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.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Answered by
GPT-4o mini
To simplify the expression \( t^{400} \cdot t^{100} \) using the Quotient Rule of Integer Exponents, we apply the product rule instead. The product rule states that when multiplying like bases, you add the exponents:
\[
t^{m} \cdot t^{n} = t^{m+n}
\]
Substituting the given exponents:
\[
t^{400} \cdot t^{100} = t^{400+100} = t^{500}
\]
Thus, the simplified expression is:
\[
t^{500}
\]
So, the correct response is:
**t500**
\[
t^{m} \cdot t^{n} = t^{m+n}
\]
Substituting the given exponents:
\[
t^{400} \cdot t^{100} = t^{400+100} = t^{500}
\]
Thus, the simplified expression is:
\[
t^{500}
\]
So, the correct response is:
**t500**
Answered by
GPT-4o mini
To simplify the expression \( a^{67}b^{34} \), we need to check if there are any common terms that can be reduced or if there's any operation implied that would change the form.
Since the expression is already in its simplest form—there are no operations (like division or multiplication by another term) being performed on it—the expression remains:
\[
a^{67}b^{34}
\]
Thus, the correct response is:
**a67b34**
Since the expression is already in its simplest form—there are no operations (like division or multiplication by another term) being performed on it—the expression remains:
\[
a^{67}b^{34}
\]
Thus, the correct response is:
**a67b34**
Answered by
GPT-4o mini
To simplify the expression \( \frac{23^{65}}{23^{32}} \) using the Quotient Rule of Integer Exponents, we apply the rule that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we have \( m = 65 \) and \( n = 32 \):
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33}
\]
Therefore, the simplified expression is:
\[
23^{33}
\]
Thus, the correct response is:
**23 superscript 33 baseline**
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we have \( m = 65 \) and \( n = 32 \):
\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33}
\]
Therefore, the simplified expression is:
\[
23^{33}
\]
Thus, the correct response is:
**23 superscript 33 baseline**
Answered by
GPT-4o mini
To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we will apply it to each base.
However, it appears that the bases are not the same. Let's rewrite the expression in the correct mathematical form:
Given the expression is:
\[
\frac{5^{53}}{5^{3}}
\]
We can simplify it using the Quotient Rule:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, we have:
\[
\frac{5^{53}}{5^{3}} = 5^{53 - 3} = 5^{50}
\]
This means the expression simplifies to:
**5 superscript 50 baseline.**
However, if you had \(5^{106}\) instead, we would have \(5^{106 - 3} = 5^{103}\), but it seems to be less relevant here. Based on the options given:
The response doesn't match with options as you provided, but assuming that it should be \(5^{50}\). Please check your options for typing errors since only \(5^{106}\) seems logical under division factual terms.
If you meant to put different exponents, please clarify.
However, it appears that the bases are not the same. Let's rewrite the expression in the correct mathematical form:
Given the expression is:
\[
\frac{5^{53}}{5^{3}}
\]
We can simplify it using the Quotient Rule:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, we have:
\[
\frac{5^{53}}{5^{3}} = 5^{53 - 3} = 5^{50}
\]
This means the expression simplifies to:
**5 superscript 50 baseline.**
However, if you had \(5^{106}\) instead, we would have \(5^{106 - 3} = 5^{103}\), but it seems to be less relevant here. Based on the options given:
The response doesn't match with options as you provided, but assuming that it should be \(5^{50}\). Please check your options for typing errors since only \(5^{106}\) seems logical under division factual terms.
If you meant to put different exponents, please clarify.
Answered by
GPT-4o mini
The correct steps to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
1. **Check if the bases are the same.**
2. **If they are, subtract the exponents of the numerator and denominator.**
3. **Write the resulting expression in exponential form.**
Thus, the correct response is:
**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.**
1. **Check if the bases are the same.**
2. **If they are, subtract the exponents of the numerator and denominator.**
3. **Write the resulting expression in exponential form.**
Thus, the correct response is:
**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.**
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