Question

simplify. express your answer using positive exponents.
$\frac{6tu^{5}v^{4}}{6t^{8}uv}$

Explanation:

Step1: Cancel out the common factor 6

$\frac{6tu^{5}v^{4}}{6t^{8}uv}=\frac{tu^{5}v^{4}}{t^{8}uv}$

Step2: Use the quotient - rule of exponents $a^m\div a^n=a^{m - n}$ for $t$ terms

$\frac{t}{t^{8}}=t^{1-8}=t^{-7}=\frac{1}{t^{7}}$

Step3: Use the quotient - rule of exponents for $u$ terms

$\frac{u^{5}}{u}=u^{5 - 1}=u^{4}$

Step4: Use the quotient - rule of exponents for $v$ terms

$\frac{v^{4}}{v}=v^{4 - 1}=v^{3}$

Step5: Combine the results

$\frac{tu^{5}v^{4}}{t^{8}uv}=\frac{u^{4}v^{3}}{t^{7}}$

Answer:

$\frac{u^{4}v^{3}}{t^{7}}$