Question

b. \\(\frac{a^{3}b^{-4}}{c^{-2}}\\)\\(\frac{a^{3}b^{-4}}{c^{-2}} = \\) (\\(\frac{a^{3}}{1}\\))(---)(---) write as product of fractions\\(=\\) apply negative exponent rule\\(=\\) multiply

Explanation:

Step1: Write as product of fractions

We can rewrite the expression \(\frac{a^{3}b^{-4}}{c^{-2}}\) as a product of three fractions: \(\frac{a^{3}}{1} \cdot \frac{b^{-4}}{1} \cdot \frac{1}{c^{-2}}\).

Step2: Apply Negative Exponent rule

Recall the negative exponent rule: \(x^{-n}=\frac{1}{x^{n}}\) and \(\frac{1}{x^{-n}} = x^{n}\). So, \(\frac{b^{-4}}{1}=\frac{1}{b^{4}}\) and \(\frac{1}{c^{-2}}=c^{2}\). Substituting these back, we get \(\frac{a^{3}}{1} \cdot \frac{1}{b^{4}} \cdot c^{2}\).

Step3: Multiply

Multiply the fractions and the variable with positive exponents together. We have \(\frac{a^{3}c^{2}}{b^{4}}\).

Answer:

\(\frac{a^{3}c^{2}}{b^{4}}\)