Question

simplify.
$(-5x^{3}y)^{3}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((-5x^{3}y)^{3}\), we can apply this rule to each factor: \((-5)^{3}(x^{3})^{3}(y)^{3}\).

Step2: Calculate each power

• Calculate \((-5)^{3}\): \((-5)\times(-5)\times(-5)= -125\).
• Calculate \((x^{3})^{3}\) using the power of a power rule \((a^m)^n=a^{mn}\), so \((x^{3})^{3}=x^{3\times3}=x^{9}\).
• Calculate \(y^{3}\) (since \(y = y^{1}\), \((y^{1})^{3}=y^{3}\)).

Step3: Multiply the results together

Multiply the three results: \(-125\times x^{9}\times y^{3}=-125x^{9}y^{3}\).

Answer:

\(-125x^{9}y^{3}\)