Question

ab³c⁵·6ca²b⁴

Explanation:

Step1: Rearrange terms by like bases

Rearrange the terms so that the coefficients and like bases are grouped together: \(1\times6\times a\times a^{2}\times b^{3}\times b^{4}\times c^{5}\times c\)

Step2: Multiply coefficients and use exponent rule \(x^m \cdot x^n = x^{m + n}\) for like bases

• Coefficients: \(1\times6 = 6\)
• For \(a\): \(a^{1+2}=a^{3}\) (using \(a = a^{1}\) and \(x^m \cdot x^n=x^{m + n}\))
• For \(b\): \(b^{3 + 4}=b^{7}\)
• For \(c\): \(c^{5+1}=c^{6}\) (using \(c = c^{1}\))

Step3: Combine the results

Multiply the coefficient with the variables: \(6a^{3}b^{7}c^{6}\)

Answer:

\(6a^{3}b^{7}c^{6}\)