Question

question
fully simplify:
$(3x^4y^3)^2$
answer attempt 1 out of 5
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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, for \((3x^{4}y^{3})^{2}\), we can apply this rule to each factor inside the parentheses: \(3^{2}(x^{4})^{2}(y^{3})^{2}\).

Step2: Simplify each term

• For the coefficient: \(3^{2}=9\).
• For the \(x\)-term: Using the power of a power rule \((a^m)^n = a^{mn}\), we have \((x^{4})^{2}=x^{4\times2}=x^{8}\).
• For the \(y\)-term: Similarly, \((y^{3})^{2}=y^{3\times2}=y^{6}\).

Step3: Combine the simplified terms

Multiply the simplified coefficient and the simplified variable terms together: \(9\times x^{8}\times y^{6}=9x^{8}y^{6}\).

Answer:

\(9x^{8}y^{6}\)