Question

va rog frumos exercitiile acestea!Multumesc, dau coronita <3​

Answer 1

Răspuns:

a) =8 ¹⁵⁻¹²=8³=(2³)³=2³ˣ³=2⁹=512

b) = 13³¹⁻³⁰+13=13¹+13=26

c) = 7²⁹⁻²⁶-7²=7³-7²=343-49=294

d) = 7¹⁷⁻¹³-7³+1=7⁴-7³=2401-343=2058

e) = 15²²⁻²⁰-1= 15²-1=225-1=224

f) = 3²·(3²)¹⁸:(3³)⁶=3²·3³⁶:3¹⁸=3²⁺³⁶⁻¹⁸=3²⁰

Answer 2

Răspuns:

Explicație pas cu pas:

$\bf a)~8^{15}: 8^{12}= 8^{15-12}= 8^{3}$

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$\bf b)~13^{31}: 13^{30}+13= 13^{31-30}+13= 13^{1}+13=26$

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$\bf c)~7^{29}: 7^{26}-7^{2}= 7^{29-26}-7^{2}=7^{2}\cdot (7^{3-1}-7^{2-2})=7^{2}\cdot 7=7^{3}$

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$\bf d)~7^{17}: 7^{13}-7^{3}+13^{0}= 7^{17-13}-7^{3}+1=$

$\bf 7^{4}-7^{3}+1=7^{3}\cdot(7^{4-3}-7^{3-3})+1=7^{3}\cdot(7^{1}-7^{0})+1=$

$\bf 7^{3}\cdot(7^{1}-7^{0})+1= 7^{3}\cdot(7-1)+1=7^{3}\cdot 6+1=$

$\bf 343\cdot 6+1=2058+1=2059$

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$\bf e)~(11+4)^{22}: 15^{20}-15^{0}= 15^{22}: 15^{20}-1=$

$\bf 15^{22-20}-1=15^{2}-1=225-1=224$

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$\bf f)~(42:14)^{2}\cdot9^{18}:27^{6}= 3^{2}\cdot3^{36}:3^{18}=3^{2+36-18}=3^{20}$