Question

simplify the expression below. ((x^{8})^{3} cdot 5x^{10})

Explanation:

Step1: Apply power of a power rule

To simplify \((x^{8})^{3}\), we use the power of a power rule \((a^{m})^{n}=a^{m\times n}\). Here, \(a = x\), \(m = 8\), and \(n=3\). So, \((x^{8})^{3}=x^{8\times3}=x^{24}\).

Step2: Multiply with the other term

Now we have \(x^{24}\cdot5x^{10}\). When multiplying terms with the same base, we use the rule \(a^{m}\cdot a^{n}=a^{m + n}\). Here, the base is \(x\), so \(x^{24}\cdot x^{10}=x^{24 + 10}=x^{34}\). And we keep the coefficient \(5\). So the simplified expression is \(5x^{34}\).

Answer:

\(5x^{34}\)