Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{4(v^{-1}s^{-1})^{-1}}{2v^{10}s^{-1}}\\)

Explanation:

Step1: Simplify the coefficient

Divide the numerical terms.
$\frac{4}{2} = 2$

Step2: Simplify the exponent of $v$

Use exponent rule $(a^m)^n=a^{mn}$ and $a^m/a^n=a^{m-n}$.
$(v^{-1})^{-1}=v^{1}$, so $\frac{v^{1}}{v^{10}} = v^{1-10}=v^{-9}$

Step3: Simplify the exponent of $s$

Use exponent rule $(a^m)^n=a^{mn}$ and $a^m/a^n=a^{m-n}$.
$(s^{-1})^{-1}=s^{1}$, so $\frac{s^{1}}{s^{-1}} = s^{1-(-1)}=s^{2}$

Step4: Convert to positive exponents

Rewrite $v^{-9}$ as $\frac{1}{v^9}$ and combine terms.
$2 \times \frac{1}{v^9} \times s^2$

Answer:

$\frac{2s^2}{v^9}$