Question

Write the expression in exponential form.
start root, start index, 2, end index, x, cubed, end root
2

x
3

​

Answer 1

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.