Question

5.1 exponent properties: p
(1 point)
multiply using the product rule:
$(2x^{11}y^{2})(4x^{14}y^{15})=$
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Explanation:

Step1: Multiply the coefficients

Multiply \(2\) and \(4\): \(2\times4 = 8\)

Step2: Apply the product rule for exponents on \(x\) - terms

For \(x^{11}\times x^{14}\), use the rule \(a^{m}\times a^{n}=a^{m + n}\). So \(x^{11}\times x^{14}=x^{11 + 14}=x^{25}\)

Step3: Apply the product rule for exponents on \(y\) - terms

For \(y^{2}\times y^{15}\), use the rule \(a^{m}\times a^{n}=a^{m + n}\). So \(y^{2}\times y^{15}=y^{2+15}=y^{17}\)

Step4: Combine the results

Combine the coefficient and the variable terms: \(8x^{25}y^{17}\)

Answer:

\(8x^{25}y^{17}\)