Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Slechts één gelijkheid is correct. Welke ?	A.	$\large \frac{\sqrt[8]{a^3}}{\sqrt[8]{\sqrt[3]{a}}}=\sqrt[3]{a}$
	B.	$\large \frac{\sqrt[6]{a}}{{\sqrt[3]{a}}}=\sqrt[3]{a}$
	C.	$\large \sqrt{a}\cdot \sqrt{a}=\sqrt[4]{a}$
	D.	$\large \sqrt[4]{\sqrt{a}}=\sqrt[6]{a}$
	E.	$\large \sqrt[5]{a}=a^{0,5}$

[ 5-1140 - op net sinds 15.10.15-(E)-3.11.2024 ]

Translation in E N G L I S H

Which equality is correct ?

Oplossing - Solution

1^ste manier :
$\frac{\sqrt[8]{a^3}}{\sqrt[8]{\sqrt[3]{a}}}=\frac{a^\frac38}{a\frac{^1}{24}}=a^{\frac{9}{24}-\frac{1}{24}}=a^{\frac{8}{24}}=a^\frac13=\sqrt[3]{a}$
2^de manier :
$\frac{\sqrt[8]{a^3}}{\sqrt[8]{\sqrt[3]{a}}}=\sqrt[8]{\frac{a^3}{\sqrt[3]{a}}}=\sqrt[8]{\frac{\sqrt[3]{a^9}}{\sqrt[3]{a}}}=\sqrt[8]{\sqrt[3]{a^8}}=\sqrt[3]{\sqrt[8]{a^8}}=\sqrt[3]{a}$