Asked by yayy
Simplify this expression using the Quotient Rule of Integer Exponents: t^400 over t^100.
t^500
t^300
300
t^4
t^500
t^300
300
t^4
Answers
Answered by
yayy
Simplify a^67 over b^34.
ab^33
a^67 over b^34
23
a^33
ab^33
a^67 over b^34
23
a^33
Answered by
yayy
Apply the Quotient Rule of Integer Exponents to simplify 23^65 divided by 23^32.
97
1^33
23^97
23^33
97
1^33
23^97
23^33
Answered by
yayy
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53 divided by 7^53.
5^106
5^53
12^106
12^53 divided by 7^53
5^106
5^53
12^106
12^53 divided by 7^53
Answered by
yayy
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
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 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.
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 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.
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 \(\frac{t^{400}}{t^{100}}\) using the Quotient Rule of Integer Exponents, we use the rule which states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = t\), \(m = 400\), and \(n = 100\). Applying the Quotient Rule:
\[
\frac{t^{400}}{t^{100}} = t^{400-100} = t^{300}
\]
So, the simplified expression is:
\[
\boxed{t^{300}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = t\), \(m = 400\), and \(n = 100\). Applying the Quotient Rule:
\[
\frac{t^{400}}{t^{100}} = t^{400-100} = t^{300}
\]
So, the simplified expression is:
\[
\boxed{t^{300}}
\]
Answered by
GPT-4o mini
To simplify the expression \(\frac{a^{67}}{b^{34}}\), we can write it as it is since it cannot be simplified further without additional context or values. Therefore, the expression remains:
\[
\frac{a^{67}}{b^{34}}
\]
From the options given, the correct answer is:
\[
\boxed{\frac{a^{67}}{b^{34}}}
\]
\[
\frac{a^{67}}{b^{34}}
\]
From the options given, the correct answer is:
\[
\boxed{\frac{a^{67}}{b^{34}}}
\]
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:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \(a = 23\), \(m = 65\), and \(n = 32\).
Applying the Quotient Rule:
\[
\frac{23^{65}}{23^{32}} = 23^{65-32} = 23^{33}
\]
So, the simplified expression is:
\[
\boxed{23^{33}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \(a = 23\), \(m = 65\), and \(n = 32\).
Applying the Quotient Rule:
\[
\frac{23^{65}}{23^{32}} = 23^{65-32} = 23^{33}
\]
So, the simplified expression is:
\[
\boxed{23^{33}}
\]
Answered by
GPT-4o mini
To simplify the expression \(\frac{12^{53}}{7^{53}}\) using the properties of exponents, we apply the rule that states \(\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m\).
Here, we can see that both the numerator and the denominator have the same exponent of 53:
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
Thus, the simplified expression is:
\[
\left(\frac{12}{7}\right)^{53}
\]
However, since none of the consequences provided in your options match this expression exactly, the best choice available is:
\[
\boxed{12^{53} \text{ divided by } 7^{53}}
\]
This means the original expression cannot be simplified further without numerical approximation or alternative forms, so it remains as is in the context of the provided options.
Here, we can see that both the numerator and the denominator have the same exponent of 53:
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
Thus, the simplified expression is:
\[
\left(\frac{12}{7}\right)^{53}
\]
However, since none of the consequences provided in your options match this expression exactly, the best choice available is:
\[
\boxed{12^{53} \text{ divided by } 7^{53}}
\]
This means the original expression cannot be simplified further without numerical approximation or alternative forms, so it remains as is in the context of the provided options.
Answered by
GPT-4o mini
The correct steps to follow 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.**
Therefore, the correct option 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.**
Therefore, the correct option 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.**