Question

Divide the following:

(1) 6⁴ ÷ 6⁷
(2) (–4)³ ÷ (–4)¹⁵
(3) ${\left(\frac{11}{12}\right)}^2÷{\left(\frac{11}{12}\right)}^3$
(4) m¹² ÷ m¹⁹
(5) a² ÷ a⁹

Answer 1

(1) 6⁴ ÷ 6⁷
$$\begin{gathered} =\frac{1}{6^{7-4}}\left(a^m÷a^n=\frac{1}{a^{n-m}}\mathrm{when}n>m\right) \\ =\frac{1}{6^3} \end{gathered}$$

(2) (–4)³ ÷ (–4)¹⁵
$$\begin{gathered} =\frac{1}{{\left(-4\right)}^{15-3}}\left(a^m÷a^n=\frac{1}{a^{n-m}}\mathrm{when}n>m\right) \\ =\frac{1}{{\left(-4\right)}^{12}} \end{gathered}$$

(3) ${\left(\frac{11}{12}\right)}^2÷{\left(\frac{11}{12}\right)}^3$
$$\begin{gathered} =\frac{1}{{\left({\displaystyle \frac{11}{12}}\right)}^{3-2}}\left(a^m÷a^n=\frac{1}{a^{n-m}}\mathrm{when}n>m\right) \\ =\frac{1}{{\left({\displaystyle \frac{11}{12}}\right)}^1} \\ =\frac{1}{\left({\displaystyle \frac{11}{12}}\right)}=\frac{12}{11} \end{gathered}$$

(4) m¹² ÷ m^{19
$$\begin{gathered} =\frac{1}{m^{19-12}}\left(a^m÷a^n=\frac{1}{a^{n-m}}\mathrm{when}n>m\right) \\ =\frac{1}{m^7} \end{gathered}$$}

(5) a² ÷ a^{9
$$\begin{gathered} =\frac{1}{a^{9-2}}\left(a^m÷a^n=\frac{1}{a^{n-m}}\mathrm{when}n>m\right) \\ =\frac{1}{a^7} \end{gathered}$$}