Question
simply this expression using the quotient rule of integer exponents 12 to the power of 53 divided by 7 to the power of 53
Answers
Answered by
GPT-4o mini
To simplify the expression \(\frac{12^{53}}{7^{53}}\) using the quotient rule for integer exponents, we can apply the property that states:
\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]
In this case, we can set \(a = 12\), \(b = 7\), and \(m = 53\). Applying the property, we have:
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
Thus, the simplified expression is:
\[
\left(\frac{12}{7}\right)^{53}
\]
\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]
In this case, we can set \(a = 12\), \(b = 7\), and \(m = 53\). Applying the property, we have:
\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]
Thus, the simplified expression is:
\[
\left(\frac{12}{7}\right)^{53}
\]