Question

Express as a single power.

Answer 1

$\\(a)\\2^3 \times 2^6 \div 2^9 = 2^{3+6} \times \dfrac{1}{2^9} = 2^9 \times 2^{-9} = 2^{9-9} = 2^0 = 1\\\\ \\(b)\\\\(-5)^8 \div (-5)^4 \times (-5)^3\\ \\= (-5)^8 \times \dfrac 1{(-5)^4 \times (-5)^3} \\\\= (-5)^8 \times \dfrac{1}{(-5)^{4+3}} \\\\= (-5)^8 \times \dfrac{1}{(-5)^7} \\\\= (-5)^{8 - 7} \\\\=(-5)^1 \\\\ =-5\\\\\\(c)\\\\\\\dfrac{6^3 \times 6^5}{6^2 \times 6^4}= \dfrac{6^{3+5}}{6^{2+4}}= \dfrac{6^8}{6^6}=6^{8-6}=6^2 =36$

Answer 2

#a

$\begin{gathered}\\ \sf\longmapsto 2^{3}×2^{6}÷2^{9}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 8+2^{-3}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 8+\frac{1}{2^{3}}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 8+\frac{1}{8}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{65}{8}\:or\:8.125\end{gathered}$