1. \( \left(-4 x^{4} y^{3} z\right)\left(-3 x y z^{4}\right)= \)

When you multiply the terms together, you start by multiplying the coefficients: \((-4) \times (-3) = 12\). Next, you combine the powers of \(x\), \(y\), and \(z\) using the rule \(a^m \cdot a^n = a^{m+n}\). So, you have: - For \(x\): \(x^4 \cdot x^1 = x^{4+1} = x^5\) - For \(y\): \(y^3 \cdot y^1 = y^{3+1} = y^4\) - For \(z\): \(z^1 \cdot z^4 = z^{1+4} = z^5\) Putting it all together, the final expression simplifies to: \[ 12 x^{5} y^{4} z^{5} \] Isn't multiplication fun? You not only bring together numbers, but also combine variables to create something new! Keep practicing those exponent rules, and you'll be solving even trickier algebra problems in no time!