Question

1. \\(\frac{3x^{3}y^{-1}z^{-1}}{x^{-4}y^{0}z^{0}}\\)

Explanation:

Step1: Simplify coefficients and variables separately

For the coefficient: it's just 3 (since the denominator has no coefficient other than 1 for the variable part, and we focus on variable exponents first, but the coefficient here is 3/1 = 3).
For \(x\): Use the rule \( \frac{a^m}{a^n}=a^{m - n} \), so \(x^{3-(-4)} = x^{3 + 4}=x^7\)
For \(y\): \(y^{-1-0}=y^{-1}=\frac{1}{y}\) (using the same exponent rule)
For \(z\): \(z^{-1-0}=z^{-1}=\frac{1}{z}\) (using the same exponent rule)

Step2: Combine all parts

Multiply the coefficient with the simplified variables: \(3\times x^7\times\frac{1}{y}\times\frac{1}{z}=\frac{3x^7}{yz}\)

Answer:

\(\frac{3x^{7}}{yz}\)