Question

simplify. express your answer using positive exponents.
$3t^{5}u^{5}v^{8} \cdot 8tu^{8}v^{9}$

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients 3 and 8.
$3\times8 = 24$

Step2: Multiply the t terms

Use the rule of exponents $a^m \cdot a^n = a^{m + n}$ for the variable \( t \). Here, \( t^5 \cdot t = t^{5+1} = t^6 \)

Step3: Multiply the u terms

Apply the exponent rule to the variable \( u \). \( u^5 \cdot u^8 = u^{5 + 8}=u^{13} \)

Step4: Multiply the v terms

Use the exponent rule for the variable \( v \). \( v^8 \cdot v^9=v^{8 + 9} = v^{17}\)

Step5: Combine all terms

Combine the coefficient and the variables with their exponents.
$24\times t^6\times u^{13}\times v^{17}=24t^6u^{13}v^{17}$

Answer:

\(24t^{6}u^{13}v^{17}\)