Let's simplify the given expression step-by-step:
Given expression:
[tex]\[
\frac{6ab}{\left(a^0 b^2\right)^4}
\][/tex]
Step 1: Simplify the denominator.
[tex]\[
\left(a^0 b^2\right)^4
\][/tex]
We use the properties of exponents here. Recall that any number raised to the power of 0 is 1, so [tex]\(a^0 = 1\)[/tex]. Hence,
[tex]\[
\left(a^0 b^2\right)^4 = \left(1 \cdot b^2\right)^4 = (b^2)^4
\][/tex]
Using the power of a power rule, [tex]\((b^2)^4 = b^{2 \cdot 4} = b^8\)[/tex].
Hence, our denominator simplifies to:
[tex]\[
b^8
\][/tex]
Step 2: Simplify the fraction.
We now have:
[tex]\[
\frac{6ab}{b^8}
\][/tex]
We can simplify this by subtracting the exponents of [tex]\(b\)[/tex] in the numerator and the denominator. Since there is a [tex]\(b\)[/tex] (which is [tex]\(b^1\)[/tex]) in the numerator, we have:
[tex]\[
b^8 = b^{8-1} = b^7
\][/tex]
So our expression becomes:
[tex]\[
\frac{6a}{b^7}
\][/tex]
Thus, the expression equivalent to the given one is:
[tex]\[
\frac{6a}{b^7}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
