To determine which expression is equivalent to [tex]\((10x)^{-3}\)[/tex], we need to simplify [tex]\((10x)^{-3}\)[/tex] step-by-step using the properties of exponents.
1. Rewrite the expression using the negative exponent property:
[tex]\[
(10x)^{-3} = \frac{1}{(10x)^3}
\][/tex]
2. Expand the denominator:
[tex]\[
(10x)^3 = 10^3 \cdot x^3
\][/tex]
3. Calculate [tex]\(10^3\)[/tex]:
[tex]\[
10^3 = 10 \times 10 \times 10 = 1000
\][/tex]
4. Substitute back into the expression:
[tex]\[
\frac{1}{(10x)^3} = \frac{1}{1000 \cdot x^3}
\][/tex]
So, [tex]\((10x)^{-3}\)[/tex] is equivalent to [tex]\(\frac{1}{1000 x^3}\)[/tex].
The correct equivalent expression among the given options is:
[tex]\[
\frac{1}{1000 x^3}
\][/tex]
