Question

Which expression is equivalent to (10x)–3?

Answer 1

many more can be expressed equivalent to it.
like
${5x \times 6x} - 3 \\ - 3 \times \sqrt{100x}$
etc.
hope it helps

Answer 2

The expression $\bold{\frac{1}{1000 x^{-3}}}$ is equivalent to$\bold{(10 x)^{-3}}.$

To find:

The expression which is equivalent to $(10 x)^{-3}$.

Solution:

We know that, the number which has a power of negative cube is equal to the reciprocal of the same number with the same power of positive cube.  

$(a)^{-3}=\left(\frac{1}{a}\right)^{3}$

Hence from the above equation, $(10 x)^{-3}$ is written as,

And as we know that the cube of 10 is 1000.

$\Rightarrow(10 x)^{-3}=\left(\frac{1}{10 x}\right)^{3}$

$=\frac{1}{(10 x) \times(10 x) \times(10 x)}$

$=\frac{1}{1000 x^{3}}$

Hence, the $\frac{1}{1000 x^{3}}$ expression is equivalent to $(10 x)^{-3}$.