Let's solve the problem step-by-step:
Given expression: [tex]\((10x)^{-3}\)[/tex]
First, we need to understand the negative exponent and how it applies to the expression inside the parentheses:
1. A negative exponent means that the base (in this case, [tex]\(10x\)[/tex]) is on the denominator.
2. The expression [tex]\((10x)^{-3}\)[/tex] can be rewritten as:
[tex]\[
\frac{1}{(10x)^3}
\][/tex]
We need to simplify [tex]\((10x)^3\)[/tex] further:
3. When raising a product to a power, you raise each factor in the product to that power:
[tex]\[
(10x)^3 = 10^3 \cdot x^3
\][/tex]
4. Calculate [tex]\(10^3\)[/tex]:
[tex]\[
10^3 = 10 \times 10 \times 10 = 1000
\][/tex]
Therefore,
[tex]\[
(10x)^3 = 1000 \cdot x^3
\][/tex]
5. Substitute this back into the fraction:
[tex]\[
\frac{1}{(10x)^3} = \frac{1}{1000 \cdot x^3}
\][/tex]
So, the simplified expression is:
[tex]\[
\frac{1}{1000 x^3}
\][/tex]
Therefore, the expression equivalent to [tex]\((10x)^{-3}\)[/tex] is:
[tex]\[
\boxed{\frac{1}{1000 x^3}}
\][/tex]
