Question

1. $\frac{r^2}{2r^3}$
2. $\frac{3n^4}{3n^3}$
3. $\frac{3m^{-4}}{m^3}$
4. $\frac{4x^0y^{-2}z^3}{4x}$

Explanation:

Problem 21: $\boldsymbol{\frac{r^2}{2r^3}}$

Step1: Use exponent rule $a^m / a^n = a^{m - n}$

$\frac{r^2}{2r^3} = \frac{1}{2} \cdot r^{2 - 3}$

Step2: Simplify the exponent

$r^{2 - 3} = r^{-1} = \frac{1}{r}$, so $\frac{1}{2} \cdot \frac{1}{r} = \frac{1}{2r}$

Step1: Cancel the common factor 3

$\frac{3n^4}{3n^3} = \frac{n^4}{n^3}$

Step2: Use exponent rule $a^m / a^n = a^{m - n}$

$n^{4 - 3} = n^1 = n$

Step1: Use exponent rule $a^m / a^n = a^{m - n}$

$3 \cdot m^{-4 - 3}$

Step2: Simplify the exponent

$m^{-7} = \frac{1}{m^7}$, so $3 \cdot \frac{1}{m^7} = \frac{3}{m^7}$

Answer:

$\frac{1}{2r}$

Problem 23: $\boldsymbol{\frac{3n^4}{3n^3}}$