Question

simplify. express your answer using positive exponents.
(8tu⁷v⁹)(2tuv⁸)

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(8\) and \(2\). So, \(8\times2 = 16\).

Step2: Multiply the \(t\) terms

For the variable \(t\), we use the rule of exponents \(a^m\times a^n=a^{m + n}\). Here, \(t^1\times t^1=t^{1 + 1}=t^2\).

Step3: Multiply the \(u\) terms

For the variable \(u\), using the same exponent rule: \(u^7\times u^1=u^{7+1}=u^8\).

Step4: Multiply the \(v\) terms

For the variable \(v\), using the exponent rule: \(v^9\times v^8 = v^{9 + 8}=v^{17}\).

Step5: Combine all the terms

Combine the coefficient and the variables: \(16\times t^2\times u^8\times v^{17}=16t^{2}u^{8}v^{17}\).

Answer:

\(16t^{2}u^{8}v^{17}\)