To find the coefficient and exponent of \( z \) in the expression \( 9x^3y^{-6}z^{-4} \times 4xy^2z^3 \), we will first multiply the two expressions together.
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Multiply the coefficients: \[ 9 \times 4 = 36 \]
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Multiply the \( x \) terms: \[ x^3 \times x^1 = x^{3+1} = x^4 \]
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Multiply the \( y \) terms: \[ y^{-6} \times y^{2} = y^{-6+2} = y^{-4} \]
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Multiply the \( z \) terms: \[ z^{-4} \times z^{3} = z^{-4+3} = z^{-1} \]
Now, combining all the parts together, we have: \[ 36x^4y^{-4}z^{-1} \]
Coefficient and Exponent of \( z \):
- Coefficient: \( 36 \)
- Exponent of \( z \): \( -1 \)
Thus, the coefficient is \( 36 \) and the exponent of \( z \) is \( -1 \).