Question

simplify the polynomial expression: \\((5x^4 y^{-1})(3x^{-2} y^3)\\)
\\(8x^2 y^2\\)
\\(15x^6 y^2\\)
\\(15x^2 y^{-2}\\)
\\(15x^2 y^2\\)

Explanation:

Step1: Multiply coefficients

Multiply the coefficients \(5\) and \(3\): \(5\times3 = 15\).

Step2: Multiply \(x\)-terms

Use the rule \(a^m\times a^n=a^{m + n}\) for \(x\)-terms: \(x^{4}\times x^{-2}=x^{4+( - 2)}=x^{2}\).

Step3: Multiply \(y\)-terms

Use the rule \(a^m\times a^n=a^{m + n}\) for \(y\)-terms: \(y^{-1}\times y^{3}=y^{-1 + 3}=y^{2}\).

Step4: Combine results

Combine the coefficient, \(x\)-term, and \(y\)-term: \(15x^{2}y^{2}\).

Answer:

D. \(15x^{2}y^{2}\) (assuming the last option is D, if options are labeled as A, B, C, D with the last one being \(15x^{2}y^{2}\))