Odpowiedź:
Szczegółowe wyjaśnienie:
1.
[tex]x=(2^3)^4=2^{12}\\y=(2^5)^4=2^{20}[/tex]
więc x<y
2.
[tex]2^2*2^3=2^5[/tex]
3.
[tex]5^{10}:5^7=5^3\\[/tex]
4.
[tex]\frac{14^4}{7^4} =(\frac{14}{7} )^4=2^4=16[/tex]
5.
[tex]10^0=1[/tex]
6.
[tex]12^2-11^2=(12-11)(12+11)=1*23=23[/tex]
7.
[tex]2^2+2^{-1}+2^0=4+\frac{1}{2} +1=5,5[/tex]
8.
10 000 000 = 10⁷
0,000 000 001= 10⁻⁹
9.
[tex](-3)^{-8}:(-3)^{-6}=(-3)^{(-8-(-6))}=(-3)^{-2}=(-\frac{1}{3} )^2=\frac{1}{9}[/tex]
10.
[tex](3^5*3^{-3})^3:3^4=(3^2)^3:3^4=3^6:3^4=3^2[/tex]
11.
[tex]\sqrt{4} +\sqrt{36} -\sqrt{49}=2+6-7=1[/tex]
12.
[tex]\sqrt{12} =\sqrt{4*3} =2\sqrt{3}[/tex]
13.
[tex]\sqrt[3]{125} -\sqrt[3]{64} =5-4=1[/tex]
Odpowiedź:
zad.1
x= (2³)⁴ = 2¹²
y = (2⁵)⁴ = 2²⁰
x < y
zad.2
2² * 2³ = 2⁵ = 32
zad.3
5¹⁰ : 5⁷ = 5³ = 125
zad.4
[tex]\frac{14^{4}}{7^{4}} = 2^{4} = 16[/tex]
zad.5
[tex]1 m = 10^{n} cm[/tex]
1 m = 100 cm
[tex]100 cm = 10^{n} cm[/tex]
n = log₁₀100
n = 2
zad. 6
12² - 11² = 144 - 121 = 23
zad. 7
2² - 2⁻¹ + 2⁰ = 4 - 1/2 + 1 = 4 1/2
zad. 8
a) 10 000 000 = 10⁷
b) 0,000 000 001 =1 * 10⁻⁹
zad. 9
(-3)⁻⁸ : (-3)⁻⁶ = (-3)⁻² = 1/9
zad. 10
(3⁵ * 3⁻³)³ : 3⁴ = (3²)³ : 3⁴ = 3⁶ : 3⁴ = 3²
zad. 11
[tex]\sqrt{4} + \sqrt{36} - \sqrt{49} = 2 + 6 - 7 = 1[/tex]
zad. 12
[tex]\sqrt{12} = \sqrt{4*3} = 2\sqrt{3}[/tex]
zad. 13
[tex]\sqrt[3]{125} - \sqrt[3]{64} = 5 - 4 = 1[/tex]