Which of the following represents 5 x to the 4 ninths power in radical form?
ninth root of 5 x to the fourth power
fourth root of 5 x to the ninth power
5 ninth root of x to the fourth power
5 fourth root of x to the ninth power

Solution:

Given

5 x to the 4 ninths power

The rule of exponents can be used to rewrite the expression,

x^a×b = x^ab

5x^4/9 = 5x^4×(1/9) 

=(5x⁴)^1/9

We can use this rule to rewrite the expression in radical form.

x^1/n = \(\sqrt[n]{x}\)

=(5x⁴)^1/9

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

Therefore,the radical form is \(\sqrt[9]{5x^{4}}\)

The correct option is the ninth root of 5 x to the fourth power.

Which of the following represents 5 x to the 4 ninths power in radical form?

Summary:

\(\sqrt[9]{5x^{4}}\) represents 5 times x to the 4 ninth power in radical form. The correct option is the ninth root of 5 x to the fourth power.