Simplify this expression using the Quotient Rule of Integer Exponents: 12 raised to the power of 53 ÷ 7 raised to the power of 53

Answer 1

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we start by applying the rule which states:

\[ \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \]

In this case, \( a = 12 \), \( b = 7 \), and \( m = 53 \). Therefore, we can rewrite the expression as follows:

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

So, the simplified expression is:

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