simplify this expression using the quotient rule of integer exponents: 12^53 divided by 7^53

12^106
5^106
5^53
12^53 divided by 7^53

1 answer

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the quotient rule of integer exponents, we can rewrite it as follows:

\[ \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \]

Now, substituting back, we have:

\[ \left(\frac{12}{7}\right)^{53} \]

Thus, the simplified expression is \( \left(\frac{12}{7}\right)^{53} \).

Among the given options, this matches with \( \frac{12^{53}}{7^{53}} \), meaning the most accurate representation of this simplified expression in the provided options is:

12^53 divided by 7^53.