Write the expression in exponential form.

start root, start index, 2, end index, x, cubed, end root
2

x
3

1 answer

The expression you've provided can be interpreted as the cube root of \( 2x^3 \). To convert this expression into exponential form, we can use the property that the cube root of a number can be expressed as that number raised to the power of \( \frac{1}{3} \).

Thus, the cube root of \( 2x^3 \) in exponential form is:

\[ (2x^3)^{\frac{1}{3}} \]

If you want to simplify it further, it can also be written as:

\[ 2^{\frac{1}{3}} \cdot (x^3)^{\frac{1}{3}} = 2^{\frac{1}{3}} \cdot x^{1} = 2^{\frac{1}{3}} x \]

So, either:

\[ (2x^3)^{\frac{1}{3}} \]

or

\[ 2^{\frac{1}{3}} x \]

is acceptable in exponential form, depending on how you want to express it.