To check whether the given equation is true or false:
[tex]\[
3 x^{-3} = \frac{1}{3 x^3}
\][/tex]
Let's rewrite both sides of the equation in terms of [tex]\(x\)[/tex].
### Left-hand side (LHS):
[tex]\[
LHS = 3 x^{-3}
\][/tex]
### Right-hand side (RHS):
[tex]\[
RHS = \frac{1}{3 x^3}
\][/tex]
We need to determine if [tex]\(LHS\)[/tex] and [tex]\(RHS\)[/tex] are equal.
### Simplifying LHS:
[tex]\[
3 x^{-3} = 3 \cdot \frac{1}{x^3} = \frac{3}{x^3}
\][/tex]
### Simplifying RHS:
[tex]\[
\frac{1}{3 x^3}
\][/tex]
Rewrite it as a single fraction:
[tex]\[
\frac{1}{3 x^3} = \frac{1}{3} \cdot \frac{1}{x^3} = \frac{1}{3x^3}
\][/tex]
Now, compare the simplified forms of the LHS and RHS:
[tex]\[
\frac{3}{x^3} \quad \text{and} \quad \frac{1}{3x^3}
\][/tex]
Clearly, these two expressions are not equal:
[tex]\[
\frac{3}{x^3} \ne \frac{1}{3 x^3}
\][/tex]
Therefore, the equation:
[tex]\[
3 x^{-3} = \frac{1}{3 x^3}
\][/tex]
is False.
