Write $(5x)^3$ as a radical expression

Key concept: A radical expression is usually used for fractional exponents. Since $(5x)^3$ has a whole-number exponent, it is already in exponential form.

Step by step

The expression

$(5x)^3$

already has an integer exponent, so it does not need to be rewritten as a radical expression.

If your teacher wants the most literal radical notation, you could write

$\sqrt[1]{(5x)^3}$

but this is not standard because it does not simplify anything.

For comparison, a true radical conversion looks like

$(5x)^{3/5}=\sqrt[5]{(5x)^3}$

Pitfall alert

Do not force an integer exponent into a radical form when the problem does not require it. Also, do not change $(5x)^3$ into a fifth root unless the exponent is actually $3/5$.

Try different conditions

If the intended expression were $(5x)^{3/5}$, the radical form would be $\sqrt[5]{(5x)^3}$. If it were $(5x)^{4/7}$, it would be $\sqrt[7]{(5x)^4}$.

Further reading

integer exponent, radical notation, rational exponent