TUGAS MTK BAB 1 BILANGAN RIIL

1. SOAL LATIHAN
1. Dengan menggunakan sifat bilangan, sederhanakan bentuk-bentuk berikut:
a) 26
x 29
b) a10
x a-9
c) (66
)5
d) 5-2
: 57
e) a8
: b-3
f) (a3
x a5
)6
2. Dengan menggunakan sifat bilangan, sedehanakan bentuk-bentuk berikut:
a) 26/5
x 21/3
b) 𝑎7/2
x 𝑎8/5
c) 32/5
x 36/6
d) 𝑏5/3
: 𝑏−7/4
e) (𝑎5/3
x 𝑎3/5
)3
3. Sederhanakan bentuk-bentuk berikut:
a) 34 + 32 - 37
b) 26 - 28 + 183
c) 55 + 204 - 452
d) 67 - 243 - 966
4. Sederhanakan perkalian-perkalian berikut ini
a) 73 x 84
b) 85 x 36
c) 3
53 x 2
74
d) 6√435
x 5√623
5. Rasionalkan pecahan berikut:
a)
2
√8
b)
3
8+ √5
c)
4
√7− √10
d)
12
√7− √6
6. Sederhanakanlah bentuk pangkat berikut:
a) (x + y)5
b) (x – y)4
c) (2x + 3y)5
d) (3x-2y)4

2. JAWABAN
1. a) 26
x 29
= 26+9
= 215
b) a10
x a-9
= a10+(-9)
= a1
c) (66
)5
= 66x5
= 630
d) 5-2
: 57
= 5(-2)-7
= 5-9
e) a8
: b-3
=
f) (a3
x a5
)6
= a3x6
x a5x6
= a18
x a30
= a18+30
= a48
2. a) 26/5
𝑥 21/3
= 2(
18+5)
15
)
= 223/15
b) 𝑎7/2
𝑥 𝑎8/5
= 𝑎
(
35+16
10
)
= 𝑎51/10
c) 32/5
𝑥 36/6
= 3(
2
5
−
1
1
)
= 3(
2−5
5
)
= 3−3/5
d) 𝑏5/3
𝑥 𝑏−7/4
= 𝑏(
20+21
12
)
= 𝑏41/12
e) (𝑎5/3
𝑥 𝑎3/5
)3
= (𝑎34/15)
)3
= 𝑎34/5
3. a) 34 + 32 - 37 = - 3
b) 26 - 28 + 183 = 22 + 29
= 27
c) 55 + 204 - 452 = 55 + 5.44 - 5.92
= 55 + 52.4 - 53.2
= 55 + 58 - 56
= 57
d) 67 - 243 - 966 = 67 + 6.43 - 6.166
= 67 + 62.3 - 64.6
= 67 + 66 - 624
= 623

3. 4. a) 73 x 84 = 8.74.3
= 5612
b) 85 x 36 = 3.86.5
= 2430
c) 3
53 x 2
74 = 527 x 716
= 7.516.27
= 35432
d) 6√435
x 5√623
= 64774.7 x 36125
= 304.2000.972
5. a)
2
√8
=
2
√8
x
√8
√8
=
2√8
8
b)
3
8+ √5
=
3
8+ √5
x
8− √5
8− √5
=
3(8− √5)
64−5
=
24−3√5
59
c)
4
√7− √10
=
4
√7− √10
x
√7+ √10
√7+ √10
=
4(√7+ √10)
7−10
=
4(√7+ √10)
−3
d)
12
√7+ √6
=
12
√7− √6
x
√7+ √6
√7+ √6
=
12(√7− √6)
7−6
=
12(√7− √6)
1
= 12(√7 − √6)
6. a) (x + y)5
= x5
+ 5x4
y + 10x3
y2
+10x2
y3
+ 5xy4
+ y5
b) (x – y)4
= x4
– 4x3
y + 6x2
y2
– 6x2
y3
+ y4
c) (2x + 3y)5
= (2x)5
+ 5(2x)4
(3y) + 10(2x)3
(3y)2
+ 10(2x)2
(3y)3
+ 5(2x)(3y)4
+ (3y)5
= 32x5
+ 5.16x4
.3y + 10.8x3
.9y2
+ 10.4x2
.27y3
+ 5.2x.81y4
+ 243y5
= 32x5
+ 240x4
y + 720x3
y2
+ 1.080x2
y3
+ 810xy4
+ 243y5

4. d) (3x-2y)4
= (3x)4
– 4(3x)3
(2y) + 6(3x)2
(2y)2
– 4(3x)(2y)3
+ (2y)4
= 81x4
– 4.27x3
.2y + 6.9x2
.4y2
– 4.3x.8y3
+ 16y4
= 81x4
– 216x3
2y + 216x2
y2
– 96xy3
+ 16y4