Let's simplify the given expression step by step:
The expression given is:
[tex]\[ \frac{6ab}{(a^0 b^2)^4} \][/tex]
1. First, we simplify the denominator:
[tex]\[
(a^0 b^2)^4
\][/tex]
2. Notice that [tex]\(a^0\)[/tex] is equal to 1 for any non-zero value of [tex]\(a\)[/tex]. So, we can rewrite the denominator as:
[tex]\[
(1 \cdot b^2)^4 = (b^2)^4
\][/tex]
3. Raise [tex]\(b^2\)[/tex] to the power of 4:
[tex]\[
(b^2)^4 = b^{2 \cdot 4} = b^8
\][/tex]
4. Now, our expression looks like this:
[tex]\[
\frac{6ab}{b^8}
\][/tex]
5. Next, we simplify by canceling common factors in the numerator and the denominator. The numerator has [tex]\(b\)[/tex] and the denominator has [tex]\(b^8\)[/tex]:
[tex]\[
\frac{6ab}{b^8} = \frac{6a \cdot b}{b^8} = \frac{6a}{b^{8-1}} = \frac{6a}{b^7}
\][/tex]
So the simplified expression is:
[tex]\[
\frac{6a}{b^7}
\][/tex]
The correct answer is:
B. [tex]\(\frac{6 a}{b^7}\)[/tex]
