Question

rewrite this measurement with a simpler unit, if possible. note: if you can simplify the unit at all, it may be possible to make more than one simplification. be sure your final answer uses the simplest possible unit. 5.6\frac{\text{kg} \cdot \text{m}^{- 3}}{\text{m}^{- 3}}

Explanation:

Step1: Analyze the unit division

We have $\frac{5.6\frac{kg\cdot m}{m^{3}}}{m^{3}}$. When dividing by a fraction, we multiply by its reciprocal. But here we can simplify the $m$ - terms in the numerator first.
The unit in the numerator $\frac{kg\cdot m}{m^{3}}=\frac{kg}{m^{2}}$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, where $a = m$, $m = 1$, and $n=3$).
So the expression becomes $5.6\frac{kg}{m^{2}\cdot m^{3}}$.

Step2: Combine the $m$ - units in the denominator

Using the rule $a^{m}\cdot a^{n}=a^{m + n}$ for $a = m$, $m = 2$, and $n = 3$, we get $m^{2}\cdot m^{3}=m^{2 + 3}=m^{5}$.
So the final unit - simplified expression is $5.6\frac{kg}{m^{5}}$.

Answer:

$5.6\frac{kg}{m^{5}}$