Question

(2x⁷)³ 8x²¹ 8x¹⁰ 6x¹⁰ 6x²¹

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((2x^7)^3\), we apply this rule: \(2^3 \times (x^7)^3\).

Step2: Calculate the powers

First, calculate \(2^3\), which is \(8\). Then, for \((x^7)^3\), we use the power of a power rule \((a^m)^n = a^{m \times n}\), so \((x^7)^3 = x^{7 \times 3} = x^{21}\).

Step3: Combine the results

Multiply the two results together: \(8 \times x^{21} = 8x^{21}\).

Answer:

\(8x^{21}\) (corresponding to the first option, e.g., A. \(8x^{21}\) if the options are labeled A, B, C, D in order)