Final answer:
The expression B^4xB^-1/4 is simplified by adding the exponents of the same base, resulting in B^(4x - 1/4).
Step-by-step explanation:
The expression B^4xB^-1/4 involves using the rules of exponents to simplify. The key rule here is that when you multiply expressions with the same base, you add the exponents. Therefore, 4x - 1/4 would be the new exponent for the base B. Another rule to consider is that when an expression has a negative exponent, it implies that the base is on the denominator, as in 1 / B^-n. Applying these rules, the expression can be rewritten as B^(4x - 1/4), assuming that x is a variable and not a multiplication sign.
To rewrite the expression in the form b^nB^4xb^-1/4, we need to consider the properties of exponents. We have: The coefficients (numbers in front of variables) are not affected by exponents, so we can write the expression as B^4xb^-1/4.
To simplify further, we can rewrite b^-1/4 as 1/b^(1/4), because a negative exponent flips the base to the denominator and an exponent of 1/4 indicates taking the fourth root.
Putting it all together, the expression can be rewritten as b^nB^4x/b^(1/4).