Question

evaluate. write your answer as a whole number or as a simplified fraction.\\(\frac{3^{-3}}{3^{0}} = \frac{\quad}{\quad}\\)

Explanation:

Step1: Apply zero exponent rule

Any non-zero number to the 0 power is 1, so $3^0 = 1$. The expression becomes $\frac{3^{-3}}{1} = 3^{-3}$.

Step2: Apply negative exponent rule

A negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$. So $3^{-3} = \frac{1}{3^3}$.

Step3: Calculate the denominator

$3^3 = 3 \times 3 \times 3 = 27$.

Answer:

$\frac{1}{27}$