Direction (41–52): What will come in the place of (?) mark in following question?

${?}^3\times 6+\sqrt[3]{512}=170$

The correct option is 3.

To find the value that comes in place of the question mark (?), we can write the equation as:
$x^3\times 6+\sqrt[3]{512}=170$
where $x$ represents the unknown value (?).

First, we evaluate the cube root of 512:
Since $8^3=8\times 8\times 8=512$, we have:
$\sqrt[3]{512}=8$

Substitute this value back into the original equation:
$x^3\times 6+8=170$

Subtract 8 from both sides of the equation to isolate the term with $x$:
$x^3\times 6=170-8$
$x^3\times 6=162$

Now, divide both sides of the equation by 6:
$x^3=\frac{162}{6}$
$x^3=27$

To find $x$, take the cube root of both sides:
$x=\sqrt[3]{27}$
Since $3^3=27$, we find:
$x=3$

Thus, the value that should come in place of the question mark is 3.