Question

1. \\(dfrac{3m^{-4}}{m^{3}}\\)

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $\frac{m^a}{m^b}=m^{a-b}$. Here, the base is $m$, so we calculate the exponent of $m$ as $-4 - 3$.
$\frac{3m^{-4}}{m^3}=3m^{-4-3}$

Step2: Simplify the exponent

Compute $-4 - 3$ to get the new exponent for $m$.
$3m^{-7}$

Step3: Rewrite with positive exponent

Use the rule $m^{-n}=\frac{1}{m^n}$ to convert to positive exponent form.
$3 \cdot \frac{1}{m^7}=\frac{3}{m^7}$

Answer:

$\frac{3}{m^7}$ (or $3m^{-7}$)