Write the expression in exponential form.

Question

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.