Evaluate the Fraction (12³)/(23³): Cube Number Division

Insert the corresponding expression:

$\frac{12^3}{23^3}=$

To solve this problem, we recognize the application of exponent rules for powers of fractions. The expression $\frac{12^3}{23^3}$ can be rewritten by using the formula $\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$.

Let's apply this to the given problem:

• Step 1: Identify the structure as $\frac{a^m}{b^m}$, where $a = 12$, $b = 23$, and $m = 3$.
• Step 2: Use the formula $\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$ to transform $\frac{12^3}{23^3}$ into $\left(\frac{12}{23}\right)^3$.

The expression $\frac{12^3}{23^3}$ simplifies to $\left(\frac{12}{23}\right)^3$.

Therefore, the correct corresponding expression is $\left(\frac{12}{23}\right)^3$.