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Simplify the expression.

10x ^-3 y^4 z^2/5x^-4y^3



A. 2xyz^2

B. 2x ^-7y^7z^2

C. 5x^12y^12z^2

D. 5xyz^2

1 answer

To simplify the expression \(\frac{10x^{-3} y^4 z^2}{5x^{-4} y^3}\), we can break it down step by step.

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

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

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

  4. The \(z\) term remains the same since there is no \(z\) in the denominator: \[ z^{2} \]

Now, combine all the simplified parts: \[ 2 \cdot x^{1} \cdot y^{1} \cdot z^{2} = 2xyz^{2} \]

Thus, the simplified expression is: \[ \boxed{2xyz^2} \]

The answer is A.