Ths Simplified from of `(b ^(3)x ^(2) a ^(4) z^(2)) ^(**)(b^ (4) x ^(3) a ^(3) z ^(3))//(a ^(2) b ^(4) z ^(3))` is

Options

A. `b ^(2) x ^(4) a ^(6)z`
B. `b ^(3) x ^(2) a ^(4) z ^(3)`
C. `b ^(x) x ^(5) a ^(5) z ^(2)`
D. `b ^(3) a ^(5) z ^(2)`

Answer

To simplify the expression \((b^{3}x^{2}a^{4}z^{2})^{(b^{4}x^{3}a^{3}z^{3})} \div (a^{2}b^{4}z^{3})\), we can follow these steps:

### Step 1: Write the expression clearly
The expression we need to simplify is:
\[ \frac{(b^{3}x^{2}a^{4}z^{2})^{(b^{4}x^{3}a^{3}z^{3})}}{(a^{2}b^{4}z^{3})} \]

### Step 2: Simplify the numerator
In the numerator, we have \((b^{3}x^{2}a^{4}z^{2})^{(b^{4}x^{3}a^{3}z^{3})}\). This means we need to multiply the exponents of each variable by the exponent in the parentheses.

- For \(b\): \(3 \cdot 4 = 12\)
- For \(x\): \(2 \cdot 3 = 6\)
- For \(a\): \(4 \cdot 3 = 12\)
- For \(z\): \(2 \cdot 3 = 6\)

So, the numerator simplifies to:
\[ b^{12}x^{6}a^{12}z^{6} \]

### Step 3: Write the complete expression
Now, we can rewrite the complete expression as:
\[ \frac{b^{12}x^{6}a^{12}z^{6}}{a^{2}b^{4}z^{3}} \]

### Step 4: Simplify the fraction
Now we will simplify the fraction by subtracting the exponents of like bases in the numerator and denominator.

- For \(b\): \(12 - 4 = 8\)
- For \(x\): \(6 - 0 = 6\) (there's no \(x\) in the denominator)
- For \(a\): \(12 - 2 = 10\)
- For \(z\): \(6 - 3 = 3\)

So, the simplified form of the expression is:
\[ b^{8}x^{6}a^{10}z^{3} \]

### Final Answer
Thus, the simplified form of the given expression is:
\[ b^{8}x^{6}a^{10}z^{3} \]