Question

question
fully simplify.
$(6x^4y^3)^4$
answer attempt 1 out of 5

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 \((6x^{4}y^{3})^{4}\) as follows:
\((6x^{4}y^{3})^{4}=6^{4}\times(x^{4})^{4}\times(y^{3})^{4}\)

Step2: Simplify each term

• For the constant term: \(6^{4}=6\times6\times6\times6 = 1296\)
• For the \(x\)-term: Using the power of a power rule \((a^{m})^{n}=a^{mn}\), we have \((x^{4})^{4}=x^{4\times4}=x^{16}\)
• For the \(y\)-term: Similarly, \((y^{3})^{4}=y^{3\times4}=y^{12}\)

Step3: Combine the simplified terms

Multiply the simplified constant, \(x\)-term, and \(y\)-term together:
\(6^{4}\times(x^{4})^{4}\times(y^{3})^{4}=1296x^{16}y^{12}\)

Answer:

\(1296x^{16}y^{12}\)