Question

$-3x^{-2}y^{5}z^{4}(-2x^{3}y^{-3})$

Explanation:

Step1: Multiply the coefficients

Multiply -3 and -2.
$$(-3)\times(-2) = 6$$

Step2: Multiply the \(x\)-terms

Use the rule \(a^m\times a^n=a^{m + n}\) for \(x^{-2}\) and \(x^3\).
$$x^{-2}\times x^3=x^{-2 + 3}=x^{1}=x$$

Step3: Multiply the \(y\)-terms

Use the rule \(a^m\times a^n=a^{m + n}\) for \(y^{5}\) and \(y^{-3}\).
$$y^{5}\times y^{-3}=y^{5+(-3)}=y^{2}$$

Step4: The \(z\)-term remains

The \(z\)-term is \(z^{4}\) as there is no other \(z\)-term to multiply with.

Step5: Combine all the terms

Multiply the results from Step1, Step2, Step3 and the \(z\)-term.
$$6\times x\times y^{2}\times z^{4}=6xy^{2}z^{4}$$

Answer:

\(6xy^{2}z^{4}\)