Simplify the expression.

Question

10x^(-3)y^(4)z^(2) over 5x^(-4)y^(3)

A. 2xyz^(2)
B. 2^(-7)y^(7)z^(2)
C. 5x^(12)y^(12)z^(2)
D. 5xyz^(2)

Answer 1

To simplify the expression \(\frac{10x^{-3}y^{4}z^{2}}{5x^{-4}y^{3}}\), we can follow these steps:

1. Divide the coefficients: \[ \frac{10}{5} = 2 \]

2. Simplify the \(x\) terms using the property of exponents \(a^m / a^n = a^{m-n}\): \[ x^{-3} / x^{-4} = x^{-3 - (-4)} = x^{-3 + 4} = x^{1} \]

3. Simplify the \(y\) terms: \[ y^{4} / y^{3} = y^{4 - 3} = y^{1} \]

4. The \(z\) term is unaffected because it only appears in the numerator: \[ z^{2} / 1 = z^{2} \]

Now, putting everything together:

\[ \frac{10x^{-3}y^{4}z^{2}}{5x^{-4}y^{3}} = 2x^{1}y^{1}z^{2} = 2xyz^{2} \]

Thus, the simplified expression is:

\[ \boxed{2xyz^{2}} \]

The correct answer is A. 2xyz^(2).