Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

16³² gedeeld door 32¹⁶ is gelijk aan	A. 1
B. 64⁸
C.
D. 2⁻¹⁶
E. 16^− 16

If you divide 16³² by 32¹⁶ the result can be written as	A. 1
	B. 64⁸
	C.
	D. 2⁻¹⁶
	E. 16^− 16

1^ste manier :
$\frac{16^{32}}{32^{16}}=\frac{(2^4)^{32}}{(2^5)^{16}}=\frac{2^{128}}{2^{80}}=2^{48}=(2^6)^8=64^8$
2^de manier :
$\frac{16^{32}}{32^{16}}=\frac{16^{32}}{2^{16}.16^{16}}=\frac{16^{16}}{2^{16}}=\left(\frac{16}{2}\right)^{16}=8^{16}=(8^2)^8=64^8$
3^de manier :
$\frac{16^{32}}{32^{16}}=\frac{(16^4)^8}{(32^2)^8}=\left(\frac{16^4}{32^2}\right)^8=\left(\frac{16^4}{16^2.2^2}\right)^8=\left(\frac{16^2}{2^2}\right)^8=(8^2)^8=64^8$