Question

Which of the following represents... in radical form?

Answer 1

The exponent is only on x, so the 5 stays out. Now when you convert fractions exponents into radicals, they become this:


`x^{(m)/(n)} = \sqrt[n]{x^m}`

So
`5x^{(4)/(9)} = 5 \sqrt[9]{x^4}`

Which would be option C).

Answer 2

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{(m)/(n)}`

`\sqrt[9]{x^4}=x^{(4)/(9)}`

`5\sqrt[9]{x^4}=5x^{(4)/(9)}`

Thus

`5x^{(4)/(9)}=5(x^4)^(1/9)`

`=5\sqrt[9]{x^4}`