Question

simplify, leave answe

1. $(4s^{3}t^{-3})^{2} =$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((4s^{3}t^{-3})^{2}\), we can apply this rule to each factor inside the parentheses:
\((4s^{3}t^{-3})^{2}=4^{2}\times(s^{3})^{2}\times(t^{-3})^{2}\)

Step2: Simplify each term

• Simplify \(4^{2}\): \(4^{2} = 16\)
• Simplify \((s^{3})^{2}\) using the power of a power rule \((a^m)^n=a^{mn}\): \((s^{3})^{2}=s^{3\times2}=s^{6}\)
• Simplify \((t^{-3})^{2}\) using the power of a power rule: \((t^{-3})^{2}=t^{-3\times2}=t^{-6}\)
• Recall that \(a^{-n}=\frac{1}{a^{n}}\), so \(t^{-6}=\frac{1}{t^{6}}\)

Putting it all together, we have:
\(4^{2}\times(s^{3})^{2}\times(t^{-3})^{2}=16\times s^{6}\times t^{-6}=\frac{16s^{6}}{t^{6}}\)

Answer:

\(\frac{16s^{6}}{t^{6}}\)