Question

1. $(8k^{2}j^{12})^{2}(4k^{-4}j^{3})$

Explanation:

Step1: Apply power of a product rule

First, apply the power of a product rule \((ab)^n = a^n b^n\) to \((8k^{2}j^{12})^{2}\).

$$
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Step2: Multiply with the other term

Now, multiply \(64k^{4}j^{24}\) with \(4k^{-4}j^{3}\). When multiplying terms with the same base, we add the exponents (for \(k\) and \(j\)) and multiply the coefficients.
For the coefficients: \(64\times4 = 256\)
For the \(k\) terms: \(k^{4}\times k^{-4}=k^{4 + (-4)}=k^{0}=1\) (since \(a^{m}\times a^{n}=a^{m + n}\) and \(a^{0}=1\) for \(a
eq0\))
For the \(j\) terms: \(j^{24}\times j^{3}=j^{24 + 3}=j^{27}\)
Multiply all these results together: \(256\times1\times j^{27}=256j^{27}\)

Answer:

\(256j^{27}\)