Question
Simplify:
$\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
$\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
✓
Answer
We have,
$\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
$=\Big(\frac{\sqrt{2}}{5}\Big)^8\times\Big(\frac{5}{\sqrt{2}}\Big)^{13}$
$=\frac{(\sqrt{2})^8}{5^8}\times\frac{5^{13}}{(\sqrt{2})^{13}}$
$=\frac{5^{13}\times5^{-8}}{(\sqrt{2})^{13}\times(\sqrt{2})^{-8}}$
$=\frac{5^{13-8}}{(\sqrt{2})^{13-8}}$
$=\frac{5^5}{(\sqrt{2})^5}=\frac{3125}{4\sqrt{2}}$
$\Rightarrow\Big(\frac{\sqrt{2}}{5}\Big)\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}=\frac{3125}{4\sqrt{2}}$
$\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
$=\Big(\frac{\sqrt{2}}{5}\Big)^8\times\Big(\frac{5}{\sqrt{2}}\Big)^{13}$
$=\frac{(\sqrt{2})^8}{5^8}\times\frac{5^{13}}{(\sqrt{2})^{13}}$
$=\frac{5^{13}\times5^{-8}}{(\sqrt{2})^{13}\times(\sqrt{2})^{-8}}$
$=\frac{5^{13-8}}{(\sqrt{2})^{13-8}}$
$=\frac{5^5}{(\sqrt{2})^5}=\frac{3125}{4\sqrt{2}}$
$\Rightarrow\Big(\frac{\sqrt{2}}{5}\Big)\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}=\frac{3125}{4\sqrt{2}}$
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