Question
Apply the quotient rule of integer exponents to simplify 12^53 divided by 7^53
Answers
GPT-4o mini
To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the properties of exponents, specifically the quotient rule, we can rewrite it as follows:
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
This uses the property of exponents that states:
\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]
So, the simplified form of \( \frac{12^{53}}{7^{53}} \) is:
\[
\left(\frac{12}{7}\right)^{53}
\]
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
This uses the property of exponents that states:
\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]
So, the simplified form of \( \frac{12^{53}}{7^{53}} \) is:
\[
\left(\frac{12}{7}\right)^{53}
\]