Answer:
[tex] b^{\frac{4}{9}} [/tex]
Step-by-step explanation:
The definition of a rational exponent:
[tex] a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m [/tex]
A quantity is raised to an exponent that is a fraction. A fractional exponent is a root. The denominator of the fraction is the index of the root. The numerator of the fraction is an exponent.
Here you just work backwards. 9 is index of the root, so it becomes the denominator of the fractional exponent. 4 is an exponent, so it becomes the numerator of the fractional exponent. b is in the root, so b is the quantity raised to the fractional exponent.
[tex] \sqrt[9]{b^4} = b^{\frac{4}{9}} [/tex]
