To multiply the expressions \(9x^3y^{-6}z^{-4}\) and \(4xy^2z^3\), you follow the rules of multiplying coefficients and combining like terms for the variables.
Here’s the step-by-step multiplication:
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Multiply the coefficients: \[ 9 \times 4 = 36 \]
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Combine the \(x\) terms: \[ x^3 \times x^1 = x^{3+1} = x^4 \]
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Combine the \(y\) terms: \[ y^{-6} \times y^{2} = y^{-6+2} = y^{-4} \]
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Combine the \(z\) terms: \[ z^{-4} \times z^{3} = z^{-4+3} = z^{-1} \]
Putting it all together, we have: \[ 36x^4y^{-4}z^{-1} \]
This can also be rewritten to eliminate the negative exponents by expressing them as fractions: \[ \frac{36x^4}{y^4 z} \]
Thus, the final result is: \[ \frac{36x^4}{y^4 z} \]
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