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

Exponents mean repeated multiplication, not regular multiplication! $12^3$ means 12 × 12 × 12 = 1728, not 12 × 3 = 36. The exponent tells you how many times to multiply the base by itself.

You can use this formula whenever you have the same exponent in both numerator and denominator. Like $\frac{5^4}{8^4}$ or $\frac{x^2}{y^2}$. If the exponents are different, this rule doesn't apply!

The expression $\left(\frac{12}{23}\right)^3$ is the simplified form the question asks for! You don't need to calculate the decimal unless specifically requested. This form shows the mathematical relationship clearly.

Think of it as "same exponents can be factored out". When you see identical exponents on top and bottom, you can pull that exponent outside and apply it to the whole fraction: $\frac{a^3}{b^3} = \left(\frac{a}{b}\right)^3$

The rule works for any numbers with the same exponent! Whether it's $\frac{7^5}{11^5}$ or $\frac{100^2}{3^2}$, you can always rewrite as $\left(\frac{7}{11}\right)^5$ and $\left(\frac{100}{3}\right)^2$ respectively.