Question

1. \\(\frac{2h^{3}j^{-3}k^{4}}{3jk}\\)

Explanation:

Step1: Separate the coefficients and variables

We can split the fraction into the coefficient part and the variable parts for \(h\), \(j\), and \(k\) separately. So we have \(\frac{2}{3}\times\frac{h^{3}}{1}\times\frac{j^{-3}}{j}\times\frac{k^{4}}{k}\).

Step2: Apply the exponent rule for division (\(a^m\div a^n = a^{m - n}\)) to each variable

• For \(h\): Since there is no \(h\) in the denominator, \(h^{3}\div1=h^{3}\).
• For \(j\): Using the rule \(a^m\div a^n=a^{m - n}\), we have \(j^{-3}\div j^{1}=j^{-3 - 1}=j^{-4}=\frac{1}{j^{4}}\) (using the rule \(a^{-n}=\frac{1}{a^{n}}\)).
• For \(k\): Using the rule \(a^m\div a^n=a^{m - n}\), we have \(k^{4}\div k^{1}=k^{4 - 1}=k^{3}\).

Step3: Combine the results

Multiply the coefficient and the simplified variable parts together: \(\frac{2}{3}\times h^{3}\times\frac{1}{j^{4}}\times k^{3}=\frac{2h^{3}k^{3}}{3j^{4}}\)

Answer:

\(\frac{2h^{3}k^{3}}{3j^{4}}\)