To determine which fraction is equivalent to [tex]\( 3^{-3} \)[/tex], we need to understand the concept of negative exponents.
1. A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. Therefore, [tex]\( 3^{-3} \)[/tex] can be rewritten using positive exponents:
[tex]\[ 3^{-3} = \frac{1}{3^3} \][/tex]
2. Next, we calculate [tex]\( 3^3 \)[/tex]:
[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]
3. Thus, [tex]\( 3^{-3} \)[/tex] is equivalent to:
[tex]\[ 3^{-3} = \frac{1}{27} \][/tex]
So, the fraction that is equivalent to [tex]\( 3^{-3} \)[/tex] is:
[tex]\[ \frac{1}{27} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{\frac{1}{27}} \][/tex]
