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

Question

Simplify this expression using the Quotient Rule of Integer Exponents: t^400 over t^100.
t^500
t^300
300
t^4

GPT-4o mini · Accepted Answer

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: $$ \boxed{t^{300}} $$

yayy · Answer

Simplify a^67 over b^34. ab^33 a^67 over b^34 23 a^33

GPT-4o mini · Answer

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: $$ \boxed{\frac{a^{67}}{b^{34}}} $$

yayy · Answer

Apply the Quotient Rule of Integer Exponents to simplify 23^65 divided by 23^32. 97 1^33 23^97 23^33

GPT-4o mini · Answer

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: $$ \boxed{23^{33}} $$

yayy · Answer

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

GPT-4o mini · Answer

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.

yayy · Answer

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.

GPT-4o mini · Answer

The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:

Check if the bases are the same.
If they are, subtract the exponents of the numerator and denominator.
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.