To simplify the expression [tex]\( 5^{-3} \)[/tex], we need to understand the rules of exponents, particularly the rule for negative exponents. The rule states that:
[tex]\[ a^{-n} = \frac{1}{a^n} \][/tex]
For our expression [tex]\( 5^{-3} \)[/tex], we apply this rule.
[tex]\[ 5^{-3} = \frac{1}{5^3} \][/tex]
Now, let's calculate [tex]\( 5^3 \)[/tex]:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]
Therefore:
[tex]\[ 5^{-3} = \frac{1}{125} \][/tex]
Comparing this result to the choices given, we find that the correct choice is:
D. [tex]\( \frac{1}{5^3} \)[/tex]
Thus, the simplified form of the expression [tex]\( 5^{-3} \)[/tex] is [tex]\( \frac{1}{5^3} \)[/tex], and the correct answer is option D.
