Question

question
fully simplify.
answer attempt 1 out of 2
(5x^{3}y^{2})^{3}

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((5x^{3}y^{2})^{3}\), we can apply this rule to each factor inside the parentheses.
\[
(5x^{3}y^{2})^{3}=5^{3}\times(x^{3})^{3}\times(y^{2})^{3}
\]

Step2: Simplify each term

• Calculate \(5^{3}\): \(5^{3}=5\times5\times5 = 125\)
• For \((x^{3})^{3}\), use the power of a power rule \((a^{m})^{n}=a^{mn}\). So \((x^{3})^{3}=x^{3\times3}=x^{9}\)
• For \((y^{2})^{3}\), using the power of a power rule, \((y^{2})^{3}=y^{2\times3}=y^{6}\)

Step3: Multiply the simplified terms together

Multiply the results from Step 2: \(125\times x^{9}\times y^{6}=125x^{9}y^{6}\)

Answer:

\(125x^{9}y^{6}\)