Question

1. $(-u^4v^2)^3$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, we can apply this to \((-u^4v^2)^3\) as follows:
\((-u^4v^2)^3 = (-1)^3 \cdot (u^4)^3 \cdot (v^2)^3\)

Step2: Simplify each term

• For \((-1)^3\), we know that \((-1)^3=-1\)
• For \((u^4)^3\), using the power of a power rule \((a^m)^n = a^{mn}\), we get \(u^{4\times3}=u^{12}\)
• For \((v^2)^3\), using the power of a power rule, we get \(v^{2\times3}=v^6\)

Step3: Multiply the simplified terms together

Multiplying the results from Step 2, we have: \(-1\times u^{12}\times v^6=-u^{12}v^6\)

Answer:

\(-u^{12}v^6\)