Question

simplify the expression below.
$(-2x^{12}y^{6})(8x^{13}y^{5})$

Explanation:

Step1: Multiply the coefficients

Multiply -2 and 8.
$-2\times8 = -16$

Step2: Multiply the \(x\)-terms using exponent rule \(a^m \cdot a^n = a^{m + n}\)

For \(x^{12}\) and \(x^{13}\), we add the exponents: \(12 + 13 = 25\), so \(x^{12} \cdot x^{13}=x^{25}\)

Step3: Multiply the \(y\)-terms using the same exponent rule

For \(y^{6}\) and \(y^{5}\), add the exponents: \(6 + 5 = 11\), so \(y^{6} \cdot y^{5}=y^{11}\)

Step4: Combine all the parts

Combine the coefficient, \(x\)-term, and \(y\)-term: \(-16x^{25}y^{11}\)

Answer:

\(-16x^{25}y^{11}\)