Question

1. simplify: $(7x^{3})^{2}(x^{8})^{\frac{1}{2}}$

Explanation:

Step1: Apply power of a product rule

For \((7x^{3})^{2}\), use \((ab)^n = a^n b^n\). So \(7^{2}(x^{3})^{2}=49x^{6}\).

Step2: Apply power of a power rule

For \((x^{8})^{\frac{1}{2}}\), use \((a^m)^n = a^{mn}\). So \(x^{8\times\frac{1}{2}} = x^{4}\).

Step3: Multiply the two results

Multiply \(49x^{6}\) and \(x^{4}\). Using \(a^m \cdot a^n = a^{m + n}\), we get \(49x^{6 + 4}=49x^{10}\).

Answer:

\(49x^{10}\)