Question

question
fully simplify.
$(-6x^3y^5)^4$
answer attempt 1 out of 3
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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 \((-6x^{3}y^{5})^{4}\) as follows:
\((-6x^{3}y^{5})^{4}=(-6)^{4}\cdot(x^{3})^{4}\cdot(y^{5})^{4}\)

Step2: Calculate each term

• Calculate \((-6)^{4}\):

\((-6)^{4}=(-6)\times(-6)\times(-6)\times(-6)=1296\)

• Calculate \((x^{3})^{4}\) using the power of a power rule \((a^m)^n = a^{mn}\):

\((x^{3})^{4}=x^{3\times4}=x^{12}\)

• Calculate \((y^{5})^{4}\) using the power of a power rule:

\((y^{5})^{4}=y^{5\times4}=y^{20}\)

Step3: Multiply the results together

Multiply the three results we got in Step 2:
\(1296\cdot x^{12}\cdot y^{20}=1296x^{12}y^{20}\)

Answer:

\(1296x^{12}y^{20}\)