Question

1. $6y^{6} cdot 5x^{4}y^{-6}$

Explanation:

Step1: Multiply the coefficients

Multiply 6 and 5.
\(6\times5 = 30\)

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

For \(y^6 \cdot y^{-6}\), we have \(y^{6 + (-6)} = y^0\). And any non - zero number to the power of 0 is 1, so \(y^0=1\).

Step3: Combine the results with the \(x\)-term

We have the coefficient 30, the \(x\)-term \(x^4\), and the result of the \(y\)-terms which is 1. So we multiply them together: \(30\times x^4\times1=30x^4\)

Answer:

\(30x^4\)