Change the following radical expressions to exponential expressions \$root(3)(xy)^4\$.

Understand the exponent notation: The expression \$root(3)(xy)^4\$ is in the form

\$root(n)(a)^m\$, where a = xy, m = 4, and n = 3

Apply the property of radicals and exponents:

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

Substitute the components a = xy, m = 4, and n = 3 into the property

\$root(3)(xy)^4 = (xy)^(4/3)\$

The exponential form of the radical expression \$root(3)(xy)^4\$ is \$(xy)^(4/3)\$.

This option correctly represents the conversion. From \$root(3)(xy)^4\$ to \$(xy)^(4/3)\$, where 4 is the exponent inside the radical and 3 is the index of the radical

\$(xy)^(4/3)\$

This option has the indices and exponents swapped. It represents \$root(4)(xy)^3\$ rather than \$root(3)(xy)^4\$

\$(xy)^(3/4)\$

This option has the base and exponent reversed. It represents \$(4/3)^(xy)\$, which is not equivalent to \$root(3)(xy)^4\$

\$(4/3)^(xy)\$

This option has an incorrect expression structure. It seems to incorrectly combine x, 4, and y without proper exponentiation or radical notation

\$(x4)^(3/y)\$

Option

A

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