Which expression is equivalent to a^4 · b^2 · a^(-4) · b^?

To simplify the expression ( a^4 cdot b^2 cdot a^{-4} cdot b^6 ), we can use the property of exponents that states ( x^m cdot x^n = x^{m+n} ).

1. Combine the terms with ( a ):

[

a^4 cdot a^{-4} = a^{4 + (-4)} = a^0 = 1

]

2. Now combine the terms with ( b ):

[

b^2 cdot b^6 = b^{2 + 6} = b^8

]

3. Therefore, the entire expression simplifies to:

[

1 cdot b^8 = b^8

]

So, the equivalent expression is ( b^8 ), which is not listed in your options, suggesting the provided choices may contain an error. The closest option that correctly simplifies with regards to ( b ) would be ( b^6 ), but it’s important to note that based on our work, we conclude with ( b^8 ).

Please double-check the expression or the options given. If you need further assistance, feel free to ask!