Question

5.1 exponent properties: f
(1 point)
multiply using the product rule:
$$ ( 5 x ^ { 9 } y ^ { 11 } ) ( 4 x ^ { 11 } y ^ { 6 } ) = $$
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Explanation:

Step1: Multiply the coefficients

Multiply \(5\) and \(4\).
\(5\times4 = 20\)

Step2: Apply the product rule for exponents \(a^m\times a^n=a^{m + n}\) to \(x\) - terms

For \(x\) - terms: \(x^{9}\times x^{11}\), using \(a^m\times a^n=a^{m + n}\) (where \(a = x\), \(m = 9\), \(n=11\)).
\(x^{9+11}=x^{20}\)

Step3: Apply the product rule for exponents \(a^m\times a^n=a^{m + n}\) to \(y\) - terms

For \(y\) - terms: \(y^{11}\times y^{6}\), using \(a^m\times a^n=a^{m + n}\) (where \(a = y\), \(m = 11\), \(n = 6\)).
\(y^{11 + 6}=y^{17}\)

Step4: Combine the results

Combine the coefficient and the variable - terms.
\((5x^{9}y^{11})(4x^{11}y^{6})=20x^{20}y^{17}\)

Answer:

\(20x^{20}y^{17}\)