Question

simplify ((x^2)^3 cdot x^4) with options (x^{12}), (x^6), (x^{10}), (x^8)

Explanation:

Step1: Apply power of a power rule

For \((x^{2})^{3}\), use the rule \((a^{m})^{n}=a^{mn}\). So, \((x^{2})^{3}=x^{2\times3}=x^{6}\).

Step2: Apply product of powers rule

Now, multiply \(x^{6}\) by \(x^{4}\). Use the rule \(a^{m}\cdot a^{n}=a^{m + n}\). So, \(x^{6}\cdot x^{4}=x^{6 + 4}=x^{10}\).

Answer:

\(x^{10}\) (corresponding to the orange option with \(x^{10}\))