Question

Evaluate the expression. Write fractions in simplest form. $$ \frac{3^{3}}{3^{-4}} $$

Short answer

The simplified form of \(\frac{3^{3}}{3^{-4}}\) is 2187.

Step-by-step solution

Understand the expression

We have the expression \(\frac{3^{3}}{3^{-4}}\). Here, the base \(3\) is the same and we are dividing the two, so we need to subtract the exponents according to the laws of exponents, which gives us \(3^{3 - (-4)}\).

Simplify the exponent

Subtract the exponent, which gives \(3^{3 +4}\). This simplifies to \(3^{7}\).

Evaluate the expression

To further simplify, we calculate \(3^{7}\), which equals to 2187.