Question

calculati folosind reguliile de calcul cu puteri
a) [4la puterea 5 x(-4)la puterea3]la puterea2;4la puterea5
b)[5la putere4x(-25)la puterea4]la puterea 2 ;(125) la puterea 7
c)[12 la puterea 5 ;(-6) la puterea 5] la puterea 2;2 la puterea6
d)[-5]la puterea 5x4la puterea5]la puterea 2;(-10)la puterea 9
e)[(-3)la puterea12 x (3 la puterea 5)la puterea2];(-3)la puterea 49
f)[-9la puterea 3 x3la puterea5] la puterea 6 ;(-3)la puterea 10
g)[7 la uterea 4x(-49)la puterea 4]la puterea2;(-7 la 7
puterea 3)la puterea
h)[50la puterea 5;(-10)laputerea5]la puterea2 ;(-5)la puterea 7
dau coroana

Answer 1

a) [4⁵x(-4)³]²;4⁵=[4¹⁰x(-4)⁶]:4⁵=[4¹⁰x4⁶:4⁵=4¹⁰⁺⁶⁻⁵=4¹¹=(2²)¹¹=2²²

b)[5⁴x(-25)⁴]² ;(125)⁷=[5⁴x(-5²)⁴]²:(5³)⁷=[5⁴x5⁸]²:5²¹=(5⁴⁺⁸)²:5²¹=(5¹²)²:5²¹=5²⁴:5²¹=5²⁴⁻²¹=5³

c)[12⁵;(-6)⁵] ²;2⁶=[(12)¹⁰:(-6)¹⁰]:2⁶=[(2²x6)¹⁰:6¹⁰]:2⁶=2²⁰x6¹⁰:6¹⁰:2⁶=2²⁰⁻⁵x6¹⁰⁻¹⁰=2¹⁵x6⁰=2¹⁵x1=2¹⁵

d)[-5]⁵x4⁵]²;(-10)⁹=(-5)¹⁰x4¹⁰:2⁹x(-5)⁹=(-5)¹⁰⁻⁹x(2²)¹⁰:2⁹=(-5)¹x2²⁰:2⁹=-5x2²⁰⁻⁹=-5x2¹¹

e)[(-3)¹² x (3⁵)²];(-3)⁴⁹=3¹²x3¹⁰:(-3)⁴⁹=3¹²⁺¹⁰:(-3)⁴⁹=3²²:3⁴⁹x(-1)=(-1)x3²²⁻⁴⁹=-3⁻²⁷=-1/3²⁷

f)[-9³ x3⁵]⁶ ;(-3)¹⁰=(-9)¹⁸x3³⁰:3¹⁰=9¹⁸x3³⁰⁻¹⁰=(3²)¹⁸x3²⁰=3³⁶x3²⁰=3³⁶⁺²⁰=3⁵⁶

g)[7⁴x(-49)⁴]²;(-7⁷)³=7⁸x(-49)⁸:(-7²¹)=7⁸x49⁸:(-7)²¹=7⁸x(7²)⁸:(-7)²¹=
7⁸x7¹⁶:(-7)²¹=7⁸⁺¹⁶:(-7)²¹=7²⁴:7²¹x(-1)=7²⁴⁻²¹x(-1)=-7³=-343

h)[50⁵;(-10)⁵]² ;(-5)⁷=50¹⁰:(-10)¹⁰:(-5)⁷=(5²x2)¹⁰:10¹⁰:(-5)⁷=
5²⁰x2¹⁰:(5x2)¹⁰:(-5)⁷=5²⁰x2¹⁰:5¹⁰x2¹⁰:5⁷x(-1)=
5²⁰⁻¹⁰⁻⁷x2¹⁰⁻¹⁰x(-1)=5³x2⁰x(-1)=5³x1x(-1)=-125