Question

1. solve. $7v^4 cdot 3u^2v^3 cdot 6uv$ $16u^3v^8$—squids $126u^2v^7$—igloos $16u^2v^7$—extreme sporting events $126u^3v^8$ – angry penguins

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(7\), \(3\), and \(6\). So, \(7\times3\times6 = 126\).

Step2: Multiply the \(u\)-terms

For the \(u\)-terms, we have \(u^{2}\) (from \(3u^{2}v^{3}\)) and \(u\) (from \(6uv\)). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(u^{2}\cdot u=u^{2 + 1}=u^{3}\). Note that the first term \(7v^{4}\) has no \(u\)-term, so we consider the exponent of \(u\) as \(0\) (since \(u^{0} = 1\)), but when multiplying, we only consider the non - zero exponents. So overall for \(u\)-terms: \(u^{2}\cdot u=u^{3}\).

Step3: Multiply the \(v\)-terms

For the \(v\)-terms, we have \(v^{4}\) (from \(7v^{4}\)), \(v^{3}\) (from \(3u^{2}v^{3}\)) and \(v\) (from \(6uv\)). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(v^{4}\cdot v^{3}\cdot v=v^{4+3 + 1}=v^{8}\).

Step4: Combine the results

Combine the coefficient, \(u\)-term, and \(v\)-term. So the product is \(126u^{3}v^{8}\).

Answer:

\(126u^{3}v^{8}\) (angry penguins)