Zadanie 1
B. 3*3*3*3*3
, bo:
[tex]3^5 =3*3*3*3*3[/tex]
Zadanie 2
D. [tex](1\frac{3}{4} )^2[/tex]
, bo:
[tex]{ \left( 0,3 \right) }^{ 4 } =0,0081\\ - { \left( 2\frac{1}{4} \right) }^{ 4 } = -25.62890625\\(2,25)^0=1 { \left( 1 \dfrac{ 3 }{ 4 } \right) }^{ 2 } =3.0625[/tex]
Zadanie 3
B. [tex]{ \left( -5 \right) }^{ 9 } < { \left( -5 \right) }^{ 10 }[/tex]
, bo ujemna liczba do potęgi parzystej, daje liczbe dodatnią (np (-2)^2 = -2*(-2)=4)
Zadanie 4
a) [tex]-(-\frac{1}{3} )^3+(\frac{1}{3} )^2=\frac{1}{27} +\frac{1}{9} =\frac{1}{27} +\frac{3}{27} =\frac{4}{27}[/tex]
b)
[tex]{ \left( \dfrac{ 3 }{ 5 } \right) }^{ 2 } - \dfrac{ { 3 }^{ 2 } }{ 5 } + \dfrac{ 3 }{ { 5 }^{ 2 } } =\frac{9}{25} +\frac{3}{25} -\frac{9}{5} =\frac{12}{25} -\frac{45}{25}=-\frac{33}{25}[/tex]
c) [tex]10 \cdot { \left( -0.3 \right) }^{ 3 } -0,3 \cdot { 10 }^{ 3 } =10*(-0,027)-0,3*1000=-0,27-300=299,73[/tex]
d) [tex]7^2*\frac{1}{7} -(-\frac{1}{7} )^0*(-7)^2=7+1*49=56[/tex]
Zadanie 5
a) [tex]4^5+4^5+4^5+4^5 > 4^6[/tex]
b) [tex]-15*(-15)^0 > -15^0[/tex]
c) [tex](-2)^0-0^7 > -2^0[/tex]
d) [tex](-8)^0-8^0=0^{16}[/tex]
Zadanie 6
a) cba [tex]c=4^5 < a= (-4)^{10} < a=(-6)^{10}[/tex]
b) def [tex]d=(-\frac{2}{3} )^7 < e=(\frac{2}{3} )^3 < f= (-\frac{2}{3} )^6[/tex]
Zadanie 7
C. 27/125
, bo:
[tex](\frac{3}{5} )^3=\frac{27}{125}[/tex]
Zadanie 8
D. 6
,bo:
[tex]5^0*7-9*(\frac{1}{3} )^2=1*7-9*\frac{1}{9} =7-1=6[/tex]
