Tugas kuliah

1. 1. Denganmenggunakansifatbilangansebagai berikut,sederhanakanbentuk-bentukberikut:
a) 26
x 29
= ...
→ 2(6+9)
= 215
b) a10
x a-9
= ...
→ a(10+(-9))
= a
c) (66
)5
= ...
→ 6(6 x 5)
= 630
d) 5-2
: 57
= ...
→ 5((-2)-7)
= 5-9
e) a8
: b-3
= ...
→
𝑎8
𝑏−3 = 𝑎8 𝑏3
f) (a3
x a5
)6
= ...
→ a(3+5)6
= a(8)6
= a48
2. Denganmenggunakansifatbilangansebagai berikut,sederhanakanbentuk-bentukberikut
a. 2
6
5 x 2
1
3 = ...
→ 2
(6
5
+
1
3
)
= 2(
18+5
15
)
= 2
23
15
b. 𝑎
7
2 x 𝑎
8
5 = ...
→ 𝑎(
7
2
+
8
5
)
= 𝑎(
35+16
10
)
= 𝑎
51
10
c. 3
2
5 : 3
6
6 = ...
→ 3(
2
5
−
1
1
)
= 3(
2−5
5
)
= 3
−3
5
d. 𝑏
5
3 : 𝑏
−7
4 = ...
→ 𝑏(
5
3
−
−7
4
)
= 𝑏(
20+21
12
)
= 𝑏
41
12
e. ( 𝑎
5
3 x 𝑎
3
5 )3
= ...
→ 𝑎
(5
3
+
3
5
)3
= 𝑎(
34
15
)3
= 𝑎
34
5
3. Sederhanakanlahbentuk-bentukberikut:
a) 4√3 + 2√3 − 7√3 = ⋯
→ 6√3 − 7√3 = −√3
b) 6√2 − 8√2 + 3√18 = ⋯
→ −2√2 + 3 ∙ 3√2 = 7√2
c) 5√5 + 4√20 − 2√45 = ⋯
→ 5√5 + 4 ∙ 2√5 − 2 ∙ 3√5 = 7√5
d) 7√6 − 3√24 − 6√96 = ⋯
→ 7√6 − 3 ∙ 2√6 − 6 ∙ 4√6 = −23√6
4. Sederhanakanperkalian-perkalianberikutini
a. 3√7 x 4√8 = ⋯
→ (3 ∙ 4)√7 ∙ 8 = 12√56 = 24√14
b. 5√8 x 6√3 = ⋯
→ (5 ∙ 6)√8 ∙ 3 = 30√24 = 60√6

2. c. 3∛5 x 4√7 = ⋯
→ 3 ∙ 5
1
3 x 4 ∙ 7
1
2 = 15
1
3 x 28
1
2 = 420
5
6
d. 6√435
x 5√623
= ⋯
→ (6 ∙ 5)(√435
∙ √623
) = 30√435
√623
5. Rasionalkanpecahanberikut
a)
2
√8
= ⋯
→
2
√8
x
√8
√8
=
2√8
8
=
1√8
4
b)
3
8+√5
= ⋯
→
3
8+√5
x
8−√5
8−√5
=
24−3√5
64−5
=
24−3√5
59
c)
4
√7−√10
= ⋯
→
4
√7−√10
x
√7+√10
√7+√10
=
4√7+4√10
7−10
=
4√7+4√10
−3
d)
12
√7+√6
= ⋯
→
12
√7+√6
x
√7−√6
√7−√6
=
12√7−12√6
7−6
= 12√7 − 12√6
6. Sederhanakanlahbentukpangkatberikut
a. (𝑥 + 𝑦)5
= ...
→ 𝑥5 + 5𝑥4 𝑦 + 10𝑥3 𝑦2 + 10𝑥2 𝑦3 + 5𝑥𝑦4 + 𝑦5
b. (𝑥 − 𝑦)4
= ...
→ 𝑥4 − 4𝑥3 𝑦 + 6𝑥2 𝑦2 − 4𝑥𝑦3 + 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 ∙ 9𝑥2 + 10 ∙ 4𝑥2 ∙ 27𝑦3 + 5 ∙ 2𝑥 ∙ 81𝑦4 + 243𝑦5
→ 32𝑥5 + 240𝑥4 𝑦 + 720𝑥3 𝑦2 + 1080𝑥2 𝑦3 + 810𝑥𝑦4 + 243𝑦5
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 𝑦 + 216𝑥2 𝑦2 − 96𝑥𝑦3 + 16𝑦4