Question

use the power rule and the power of a product rule to simplify the expression.\\((2q^{5})^{3}\\)\\((2q^{5})^{3}=\square\\)

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((2q^5)^3\), we apply this rule: \(2^3 \cdot (q^5)^3\).

Step2: Apply power rule

The power rule states that \((a^m)^n = a^{m \cdot n}\). For \((q^5)^3\), we have \(q^{5 \cdot 3}=q^{15}\). And \(2^3 = 8\).

Step3: Combine results

Multiply the results from Step1 and Step2: \(8 \cdot q^{15}=8q^{15}\).

Answer:

\(8q^{15}\)