To express 5 x to the 4 ninths power in radical form, we first need to understand what the exponent of 4/9 means. The fraction 4/9 indicates that we have a base raised to a power and then taking a root.
In general, the expression a^(m/n) can be converted into radical form as follows:
- The denominator (n) represents the root.
- The numerator (m) represents the power to which the base is raised.
Applying this to our expression, we can break it down:
- The base is 5x.
- The total exponent is 4/9, so this will translate to a ninth root because of the denominator 9.
- We raise to the fourth power because of the numerator 4.
In radical form, this results in:
√5x^4, which is equivalent to:
5x raised to the fourth power inside the radical of the ninth root.
Thus, we can write it as:
√[9]{(5x)^4}
So, the answer in radical form is √[9]{(5x)^4}.