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: 

$x^{\dfrac{m}{n}} = \sqrt[n]{x^m}$

So $5x^{\dfrac{4}{9}} = 5 \sqrt[9]{x^4}$

Which would be option C).

Answer 2

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}}$

$\sqrt[9]{x^4}=x^{\frac{4}{9}}$

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

Thus

$5x^{\frac{4}{9}}=5(x^4)^{1/9}$

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