Question

simplify $-5k^{4} \cdot 5j^{7} \cdot 6k^{4}$
select the correct response:
$-150kj^{15}$
$-150k^{28}j^{7}$
$6k^{8}j^{7}$
$-150k^{8}j^{7}$

Explanation:

Step1: Multiply the coefficients

Multiply \(-5\), \(5\), and \(6\). So, \(-5\times5\times6=-150\).

Step2: Multiply the \(k\)-terms

Using the rule \(a^m\cdot a^n = a^{m + n}\), for \(k^4\cdot k^4\), we have \(k^{4+4}=k^8\).

Step3: The \(j\)-term remains

The \(j^7\) term doesn't have another \(j\)-term to multiply with, so it stays as \(j^7\).

Step4: Combine all parts

Combine the coefficient, \(k\)-term, and \(j\)-term: \(-150k^8j^7\).

Answer:

\(-150k^{8}j^{7}\) (the last option: \(-150k^{8}j^{7}\))