Question

simplify the expression. your answer should only contain positive exponents.\\(\frac{3v^{0}}{u^{4}v^{-8}}\\)\
select the correct response:\
\\(\frac{2}{5u^{3}}\\)\
\\(\frac{3}{u^{4}}\\)\
\\(\frac{3}{u^{4}v^{8}}\\)\
\\(\frac{3v^{8}}{u^{4}}\\)

Explanation:

Step1: Apply zero exponent rule

Any non - zero number to the power of 0 is 1. So \(v^{0}=1\), and the expression \(\frac{3v^{0}}{u^{4}v^{-8}}\) becomes \(\frac{3\times1}{u^{4}v^{-8}}=\frac{3}{u^{4}v^{-8}}\).

Step2: Apply negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) (or \(\frac{1}{a^{-n}} = a^{n}\) for \(a
eq0\)). For the term \(v^{-8}\) in the denominator, we can rewrite it as \(v^{8}\) in the numerator. So \(\frac{3}{u^{4}v^{-8}}=\frac{3v^{8}}{u^{4}}\).

Answer:

\(\frac{3v^{8}}{u^{4}}\) (corresponding to the option \(\boldsymbol{\frac{3v^{8}}{u^{4}}}\))