Question

simplify. express your answer using
$(9x^{9})^{2}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((9x^{9})^{2}\), we can apply this rule as \(9^{2}\times(x^{9})^{2}\).

Step2: Calculate each part

First, calculate \(9^{2}\), which is \(9\times9 = 81\). Then, for \((x^{9})^{2}\), we use the power of a power rule \((a^m)^n=a^{m\times n}\), so \((x^{9})^{2}=x^{9\times2}=x^{18}\).

Step3: Combine the results

Multiply the two results together: \(81\times x^{18}=81x^{18}\).

Answer:

\(81x^{18}\)