Question

1. calculati a) 3^17 × 7^17- 21^17
b) 5^ 20 × 3^20 -15 ^21 :15
c ) 3^ 18 × 8^18 : ( 6^16 × 4^16)
d) 15^38 : 5^38 -( 3^19)^2
e)14 ^27 :7^27 :2^5^2
f) 10^64 :2^64 -5 ^4^3
g) 15 ^n+2 : 5^n+2 :3^n


2. calculati
a) 3+2 × [(2^27×3^35)^2 :(2^51×3^69)-4^17:2^33+35]
b) 3^3+3^20 :3^18+3×3^8+3^10:(8×3^5+3^5 )-4×3^3
c)[ 3+3×3^43+(7^5)^10 :7^7^2]:[9^22 +7^1^22+15^n+1 :5^n+1 :3^n]
d) 18^2+36:[ 2^8^2 : (2^9)^7+9^15:(3×3^28)]

3 . calculati a=(b-c)^2011 , unde b=[(2^3)^2- 1954^0 ] :3^2^1^7 -(4^1^2^3 - 1^4^3^2), iar c= 32×7^5-14^5+3 .


multumesc .....

Answer 1

1)
a) 3^17 × 7^17- 21^17=(3x7)¹⁷-21¹⁷=21¹⁷-21¹⁷=0
b)  5^ 20 × 3^20 -15 ^21 :15=(5x3)²⁰-15²¹⁻¹=15²⁰-15²⁰=0
c) 3^ 18 × 8^18 : ( 6^16 × 4^16)=(8x3)¹⁸:(6x4)¹⁶=24¹⁸:24¹⁶=24²=576
d) 15^38 : 5^38 -( 3^19)^2=(15:5)³⁸-3³⁸=3³⁸-3³⁸=0
e) 14 ^27 :7^27 :2^5^2=(14:7)²⁷:2¹⁰=2²⁷:2¹⁰=2²⁷⁻¹⁰=2¹⁷
f) 10^64 :2^64 -5 ^4^3=(10:2)⁶⁴-5¹²=5⁶⁴-5¹²
g) 15 ^n+2 : 5^n+2 :3^n= 15ⁿx15²:5ⁿx5²:3ⁿ=3ⁿx5ⁿx15²:5ⁿx5²:3ⁿ=15²x5²=225+25=250

2) a)
3+2 × [(2^27×3^35)^2 :(2^51×3^69)-4^17:2^33+35]=
 3+2 × [(2⁵⁴×3⁷⁰) :(2⁵¹×3⁶⁹)-2³⁴:2³³+35]=  
 3+2 × (2³×3-2³⁴:2³³+35)= 3+2x(8x3-2+35)=3+2x57=3+114=117 

b) 3^3+3^20 :3^18+3×3^8+3^10:(8×3^5+3^5 )-4×3^3=
 3³+3²+3⁹+3¹⁰:9x3⁵-4×3³=
3³+3²+3⁹+3¹⁰:3⁷-4×3³=
27+9+3⁹+3³-4x27=27+9+19683+27-108=19638