Question

simplify. express your answer using positive exponents.\\(\frac{5s^{7}tu}{5st^{5}u^{7}}\\)

Explanation:

Step1: Simplify the coefficient

The coefficient of the numerator is 5 and the coefficient of the denominator is 5. So, $\frac{5}{5} = 1$.

Step2: Simplify the variable \( s \)

For the variable \( s \), we use the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. Here, $m = 7$ and $n = 1$, so $\frac{s^{7}}{s^{1}}=s^{7 - 1}=s^{6}$.

Step3: Simplify the variable \( t \)

For the variable \( t \), $m = 1$ and $n = 5$, so $\frac{t^{1}}{t^{5}}=t^{1 - 5}=t^{- 4}$. Using the rule $a^{-n}=\frac{1}{a^{n}}$, we can rewrite it as $\frac{1}{t^{4}}$.

Step4: Simplify the variable \( u \)

For the variable \( u \), $m = 1$ and $n = 7$, so $\frac{u^{1}}{u^{7}}=u^{1 - 7}=u^{-6}$. Using the rule $a^{-n}=\frac{1}{a^{n}}$, we can rewrite it as $\frac{1}{u^{6}}$.

Step5: Combine all the simplified parts

Multiply all the simplified parts together: $1\times s^{6}\times\frac{1}{t^{4}}\times\frac{1}{u^{6}}=\frac{s^{6}}{t^{4}u^{6}}$.

Answer:

$\frac{s^{6}}{t^{4}u^{6}}$