Question

simplify. express your answer using positive exponents.
\frac{8s^{-1}t^{4}u^{0}}{2s^{0}t^{4}u}

Explanation:

Step1: Use the zero - exponent rule

Any non - zero number to the power of 0 is 1. So, $s^{0}=1$ and $u^{0}=1$. The expression becomes $\frac{8s^{- 1}t^{4}\times1}{2\times1\times t^{4}u}=\frac{8s^{-1}t^{4}}{2t^{4}u}$.

Step2: Simplify the coefficient and use the quotient rule of exponents

Simplify the coefficient $\frac{8}{2}=4$. For the variables with the same base, use the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$. For $t$, $\frac{t^{4}}{t^{4}}=t^{4-4}=t^{0}=1$. For $s$, we have $s^{-1}$ in the numerator. Using the rule $a^{-n}=\frac{1}{a^{n}}$, we rewrite $s^{-1}$ as $\frac{1}{s}$. The expression is now $\frac{4\times\frac{1}{s}}{u}$.

Step3: Write the final simplified form

$\frac{4}{su}$.

Answer:

$\frac{4}{su}$