Odpowiedzi

2010-02-06T21:38:08+01:00
Ad.1.
a) 128=2⁷
b) 343=7³
c)1/64 = 1/8² = 8⁻²
d)1/625=1/25²=25⁻²=5⁻⁴
e)1/512=1/2⁹=2⁻⁹

Ad.2 (x-mnożenie)
a) (½)⁶-(½)⁷=(½)⁶(1-½)=(½)⁶ x (½)=(½)⁷
b) 3x2⁴+2⁵+2⁶+7x2⁴=2⁴(3+2+2²+7)=2⁴x16=2⁴x2⁴=2⁸
c) 5⁸+3x25³-5⁷+2x5⁶= 5⁸+3x(5²)³-5⁷+2x5⁶=5⁸+3x5⁶-5⁷+2x5⁶=
=5⁶(5²+3-5+2)=5⁶x25=5⁶x5²=5⁸
d)2x3¹³+5x3¹¹+12x3¹⁰=3¹⁰(2x3³+5x3+12)=3¹⁰x81=3¹⁰x3⁴=3¹⁴
e - spróbuj sam

Ad.3.
a)(1½)x(1½)³=(1½)⁴=(3/2)⁴=81/16=5i1/16
b)(1¾)⁻⁴:(1¾)⁻⁶=(1¾)⁻⁴⁺⁶=(1¾)²=(7/4)²=49/16
c)4⁹:(4⁵:4⁻⁴)=4⁹:(4⁵⁺⁴)=4⁹:4⁹=4⁹⁻⁹=4⁰=1
d)(0,3)⁸x(3⅓)⁸=(0,3x3⅓)⁸=(3/10 x 10/3)⁸=1⁸=1
e)[(2⁻³)⁻²]⁻¹= (mnożymy wykładniki) = 2⁻⁷=1/2⁷=1/128
f)[(7³²x7⁶³x(7⁴)⁶]/[(7⁸)⁹x(7⁶)⁸]=[7³²x7⁶³x7²⁴] / [7⁷²x7⁴⁸]=
(7³²⁺⁶³⁺²⁴):(7⁷²⁺⁴⁸)=7¹¹⁹:7¹²⁰=7¹¹⁹⁻¹²⁰=7⁻¹=1/7
e)[5x4⁷-6x16³]/2¹³=[5x(2²)⁷-6x(2⁴)³]/2¹³=[5x2¹⁴-6x2¹²]/2¹³=
=2¹²(5x2²-6)/2¹³=(5x2²-6)/2=14/2=7

Rozwiązanie zadania 12 znajdziesz na stronie:
http://matematyka.pisz.pl/strona/1262.html