Question

below. write your answer using only positive exponents. \\(\frac{2^{-2}m^{-3}}{n^0}\\) \\(\circ\\) \\(4m^3\\) \\(\circ\\) \\(\frac{m^3}{4}\\) \\(\circ\\) \\(\frac{4}{m^3}\\) \\(\circ\\) \\(\frac{1}{4m^3}\\) clear my selection

Explanation:

Step1: Simplify \( n^0 \)

Any non - zero number to the power of 0 is 1, so \( n^0 = 1 \) (assuming \( n
eq0 \)). The expression becomes \( \frac{2^{-2}m^{-3}}{1}=2^{-2}m^{-3} \).

Step2: Simplify negative exponents

Recall the rule \( a^{-n}=\frac{1}{a^{n}} \). For \( 2^{-2} \), we have \( 2^{-2}=\frac{1}{2^{2}}=\frac{1}{4} \). For \( m^{-3} \), we have \( m^{-3}=\frac{1}{m^{3}} \).
So \( 2^{-2}m^{-3}=\frac{1}{4}\times\frac{1}{m^{3}}=\frac{1}{4m^{3}} \).

Answer:

\(\frac{1}{4m^{3}}\) (the option with this expression, which is the last option: \(\frac{1}{4m^{3}}\))