Solving Radical Expression: Simplify ⁶√b¹²×(1/b)²×a

To solve this problem, we'll follow these steps:

• Step 1: Simplify $\sqrt[6]{b^{12}}$ using fractional exponent form.
• Step 2: Simplify the expression $\left(\frac{1}{b}\right)^2$ using negative exponents.
• Step 3: Combine and simplify the entire expression.

Now, let's work through each step:

Step 1: Simplify $\sqrt[6]{b^{12}}$.
The expression $\sqrt[6]{b^{12}}$ can be rewritten using fractional exponents as $b^{12/6} = b^2$.

Step 2: Simplify $\left(\frac{1}{b}\right)^2$.
The expression $\left(\frac{1}{b}\right)^2$ simplifies using negative exponents: $b^{-2}$.

Step 3: Combine the simplified expressions and the original variable $a$.
Combine all components as follows:
$b^2 \cdot b^{-2} \cdot a$.
Using the property $x^m \cdot x^n = x^{m+n}$, we have:
$b^{2 + (-2)} \cdot a = b^0 \cdot a$.
Since $b^0 = 1$ (by the zero exponent rule), the expression simplifies to:
$a$.

Therefore, the solution to the problem is $a$.