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

Q: Can $(5x)^3$ be written as a radical expression?

Not in any standard useful way, because the exponent 3 is an integer. Radical form is mainly used for fractional exponents.

Question

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

$(5x)^3 = \sqrt[5]{5^3x^3} = \sqrt[5]{125x^3}$

$(2x)^{4/7} = \sqrt[7]{(2x)^4} = \sqrt[7]{2^4x^4} = \sqrt[7]{16x^4}$

Acemy AI · Accepted Answer

> **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

Question

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

Expert Verified Solution

Step by step

Pitfall alert

Try different conditions

Further reading

FAQ

Can $(5x)^3$ be written as a radical expression?

What is the radical form of $(5x)^{3/5}$?