Question

simplify. express your answer using positive exponents. (7y⁹z)(7y⁴z)(9y⁹z)

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(7\), \(7\), and \(9\). So, \(7\times7\times9 = 441\).

Step2: Multiply the \(y\)-terms using exponent rule

For the \(y\)-terms, we use the rule \(a^m\times a^n=a^{m + n}\). So, \(y^{9}\times y^{4}\times y^{9}=y^{9 + 4+9}=y^{22}\).

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

For the \(z\)-terms, using the same exponent rule \(a^m\times a^n=a^{m + n}\), we have \(z\times z\times z=z^{1 + 1+1}=z^{3}\).

Step4: Combine the results

Combine the coefficient, \(y\)-term, and \(z\)-term together. So the simplified form is \(441y^{22}z^{3}\).

Answer:

\(441y^{22}z^{3}\)