Question

x^{15}y^{20} cdot x^{17}y^{18}

Explanation:

Step1: Use exponent rule \(a^m \cdot a^n = a^{m + n}\) for \(x\) terms

For the \(x\) variables, we have \(x^{15} \cdot x^{17}\). Applying the rule, we add the exponents: \(15 + 17 = 32\), so this becomes \(x^{32}\).

Step2: Use exponent rule for \(y\) terms

For the \(y\) variables, we have \(y^{20} \cdot y^{18}\). Applying the same rule, we add the exponents: \(20 + 18 = 38\), so this becomes \(y^{38}\).

Step3: Combine the results

Multiplying the results for \(x\) and \(y\) together, we get \(x^{32}y^{38}\).

Answer:

\(x^{32}y^{38}\)