If `x^2 b^4=ab^(-1)` , what is a in terms of b and x ?

Options

A. `x^2 b^3`
B. `x^2 b^5`
C. `x^2 b^(-3)`
D. `x^2 b^(-5)`

Answer

To solve the equation \( x^2 b^4 = ab^{-1} \) for \( a \) in terms of \( b \) and \( x \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ x^2 b^4 = ab^{-1} \]
We can rewrite \( ab^{-1} \) as \( \frac{a}{b} \):
\[ x^2 b^4 = \frac{a}{b} \]

### Step 2: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ x^2 b^4 \cdot b = a \]
This simplifies to:
\[ a = x^2 b^5 \]

### Step 3: Write the final answer
Thus, we have expressed \( a \) in terms of \( b \) and \( x \):
\[ a = x^2 b^5 \]

### Conclusion
The correct expression for \( a \) in terms of \( b \) and \( x \) is:
\[ \boxed{x^2 b^5} \]