Question

Simplify this expression using the Quotient Rule of Integer Exponents: 12^53 divide by 7^53

A.5^106
B.5^53
C.12^53 divide by 7^53
D.12^106

Answer 1

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we can apply the rule that states:

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

In this case, we have \( a = 12 \), \( b = 7 \), and \( m = 53 \). Therefore:

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

Since none of the answer choices provided (A, B, C, or D) involve this simplified expression directly, we can look at the options more closely:

A. \( 5^{106} \)

B. \( 5^{53} \)

C. \( \frac{12^{53}}{7^{53}} \) (which is equal to our simplified form)

D. \( 12^{106} \)

The correct answer that matches our simplification is:

**C. \( \frac{12^{53}}{7^{53}} \)**