Question

9x^3y^-6z^-4 times 4xy^2z^3

Answer 1

Find the coefficient and the exponent of z

Answer 2

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:

1. **Multiply the coefficients**:
\[
9 \times 4 = 36
\]

2. **Combine the \(x\) terms**:
\[
x^3 \times x^1 = x^{3+1} = x^4
\]

3. **Combine the \(y\) terms**:
\[
y^{-6} \times y^{2} = y^{-6+2} = y^{-4}
\]

4. **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:
\[
\frac{36x^4}{y^4 z}
\]