Question

simplify the following expression using the products-to-powers rule.
$\left(-3x^{5}\
ight)^{2}$
$\left(-3x^{5}\
ight)^{2}=\square$ (simplify your answer. type your answer using exponential notation.)

Explanation:

Step1: Apply products - to - powers rule

The products - to - powers rule states that \((ab)^n=a^n\times b^n\). For the expression \((- 3x^{5})^{2}\), we can apply this rule where \(a=-3\), \(b = x^{5}\) and \(n = 2\). So we get \((-3)^{2}\times(x^{5})^{2}\).

Step2: Simplify each part

First, simplify \((-3)^{2}\). We know that \((-3)\times(-3)=9\). Then, simplify \((x^{5})^{2}\) using the power - of - a - power rule \((a^{m})^{n}=a^{m\times n}\). Here, \(a = x\), \(m = 5\) and \(n = 2\), so \((x^{5})^{2}=x^{5\times2}=x^{10}\).

Step3: Multiply the results

Multiply the two simplified parts together: \(9\times x^{10}=9x^{10}\).

Answer:

\(9x^{10}\)