Question

number 9
(5x²y)(x³y⁴z)(2y³z⁴)

Explanation:

Step1: Multiply coefficients

Multiply the numerical coefficients: \( 5 \times 1 \times 2 = 10 \).

Step2: Combine \(x\)-terms

For \(x\)-terms, use exponent rule \(a^m \cdot a^n = a^{m + n}\): \( x^2 \cdot x^3 = x^{2 + 3} = x^5 \).

Step3: Combine \(y\)-terms

For \(y\)-terms: \( y \cdot y^4 \cdot y^3 = y^{1 + 4 + 3} = y^8 \).

Step4: Combine \(z\)-terms

For \(z\)-terms: \( z \cdot z^4 = z^{1 + 4} = z^5 \).

Step5: Combine all terms

Multiply the results from steps 1 - 4: \( 10x^5y^8z^5 \).

Answer:

\( 10x^5y^8z^5 \)