Change the following exponential expressions to radical expressions \$14 x^(2/3)\$.

Understand the exponent notation: The expression \$x^(2/3)\$ is in the form

\$a^(m/n)\$, where a = x, m = 2 and n = 3

Apply the property of exponents and radicals:

\$a^(m/n) = root(n)(a)^m\$

Substitute the components a = x, m = 2, and n = 3 into the property

\$x^(2/3) = root(3)(x)^2\$

The original expression includes a constant multiplier, 14. Multiply the radical form by this constant:

\$14 x^(2/3) = 14 root(3)(x)^2\$

The radical form of the given exponential expression is \$14 root(3)(x^2)\$.

This option is incorrect because it has the correct constant (14) but the wrong index and exponent

\$14 root(2)(x^3)\$

This option is incorrect because the constant should be 14, not 3, and the index should be 3, not 14

\$3 root(14)(x^2)\$

This option is incorrect because the constant should be 14, not 2, the index should be 3, not 14, and the exponent inside the radical should be 2, not 3

\$2 root(14)(x^3)\$

This option matches the correct conversion because the constant is correct (14), the index is correct (3), and the exponent inside the radical is correct (2)

\$14 root(3)(x^2)\$

Option

D

Can you summarize what you’ve understood in the above steps?