Question

(-4x^5y^3)^3

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So we can apply this to \((-4x^{5}y^{3})^{3}\) as follows:
\((-4x^{5}y^{3})^{3}=(-4)^{3}\times(x^{5})^{3}\times(y^{3})^{3}\)

Step2: Calculate each part

First, calculate \((-4)^{3}\). We know that \((-4)\times(-4)\times(-4)= -64\).
Next, use the power of a power rule \((a^m)^n=a^{m\times n}\) for \((x^{5})^{3}\): \(x^{5\times3}=x^{15}\).
Then, use the power of a power rule for \((y^{3})^{3}\): \(y^{3\times3}=y^{9}\).

Step3: Multiply the results together

Now, multiply the three results: \((-4)^{3}\times(x^{5})^{3}\times(y^{3})^{3}=-64\times x^{15}\times y^{9}=-64x^{15}y^{9}\)

Answer:

\(-64x^{15}y^{9}\)