Which of the following represents 6x^3/4 in radical form?
\(^3\sqrt{6x^4}\)
\(^4\sqrt{6x^3}\)
\(6 \,^3\sqrt{x^4}\)
\(6 \,^4\sqrt{x^3}\)

Solution:

Given, 6x^3/4

We have to represent 6x^3/4 in radical form.

By using the property,

(x ^m) ⁿ = x ^m×n

So, \(6x^{\frac{3}{4}}={6x^3}^{\frac{1}{4}}\)

By using the property,

\(x^{\frac{m}{n}}=\sqrt[n]{x^{m}}\)

\({6x^3}^{\frac{1}{4}}=\sqrt[4]{6x^{3}}\)

Therefore, the radical form of the given expression is \(\sqrt[4]{6x^{3}}\)

This is denoted as the fourth root of 6 times x-cubed.

Which of the following represents 6x^3/4 in radical form?

Summary:

\(6\sqrt[4]{x^{3}}\) represents 6x^3/4 in radical form.