Question

what is the fractional exponent of $sqrt9{b}$?
note:
fractional exponent = rational exponent
$9^b$
$b^9$
$b$
$b^{\frac{1}{9}}$

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to a fractional (rational) exponent is $\sqrt[n]{x}=x^{\frac{1}{n}}$.

Step2: Apply the rule to $\sqrt[9]{b}$

Here, $n = 9$ and $x = b$. So, $\sqrt[9]{b}=b^{\frac{1}{9}}$.

Answer:

$b^{\frac{1}{9}}$ (the option with $b^{\frac{1}{9}}$)