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1. QUESTION AND SOLUTION
EXPONENTIAL
Written by:
SYAHLUL ERBI SYAPUTRA

2. QUESTION AND SOLUTION
1. Simplify the following questions.
Solution :
4
3
2 + 4
1
2 + 4
−1
2 + 4
−3
2
= √43 + √4 +
1
√4
+
1
√43
= 22
+ 2 +
1
2
+
1
23
= 4 + 2 +
1
2
+
1
8
=
32 + 16 + 4 + 1
8
=
53
8
2. Simple form of
(𝑥+𝑦)3𝑎+1
(𝑥+𝑦)2𝑎+5 is…
Solution :
(𝑥 + 𝑦)3𝑎+1
(𝑥 + 𝑦)2𝑎+5
= (𝑥 + 𝑦)(3𝑎+1)− (2𝑎+5)
= (𝑥 + 𝑦)3𝑎−2𝑎+1−5
= (𝑥 + 𝑦)𝑎−4
3. The simple form and the positive exponent of
𝑎𝑏−4
𝑎−2𝑏
is…
Solution :
𝑎
𝑏4
𝑏
𝑎2
=
𝑎
𝑏4
×
𝑎2
𝑏
=
𝑎3
𝑏5

3. 4. Determine the value of (8)
2
3 is…
Solution :
(8)
2
3 = √82
3
= 22
= 4
5. Determine the value of
3𝑝3𝑞3
3𝑝𝑞2
is…
Solution :
3𝑝3
𝑞3
3𝑝𝑞2
= 3𝑝(3−1)
𝑞(3−2)
= 3𝑝2
𝑞
6. Determine the value of
6𝑝8
3𝑝2×2𝑝3
is…
Solution :
6𝑝8
3𝑝2 × 2𝑝3
=
6𝑝8
6𝑝5
= 6𝑝3
7. Determine the value of √18 is..
Solution :
√18
= √9 × √2
= 3√2
8. Root form for 5
2
3 is…
Solution :
5
2
3
= √(5)2
3
= √25
3

4. 9. Determine the value of √24 × √27 × √32 is…
Solution :
√24 × √27 × √32
= √4 × 6 × √9 × 3 × √16 × 2
= 2√6 × 3√3 × 4√2
= 24√36
= 24 × 6
= 144
10. Determine the value of 127
× 12−15
is…
Solution :
127
× 12−15
= 127+(−15)
= 12−8
=
1
128
11. Determine the value of √7 + 2√12 is…
Solution :
√7 + 2√12
= √(3 + 4) + 2√3 × 4
= √3 + √4
= √3 + 2
12. Determine the value of √8 − √60 is…
Solution :
√8 − √60
= √8 − √4 × 15
= √8 − 2√15
= √(5 + 3) − 2√5 × 3
= √5 – √3

5. 13. Determine the value of √5 + √21 is…
Solution :
√5 + √21
= √
10 + 2√21
2
=
1
√2
√10 + 2√21
=
1
√2
(√(3 + 7) + 2√3 × 7)
=
1
√2
(√3 + √7)
=
1
2
√2 (√3 + √7)
=
1
2
(√6 + √14)
14. Determine the value of
𝑚
−
1
2𝑛
3
2
(𝑚3𝑛5)
is…
Solution :
𝑚−
1
2𝑛
3
2
(𝑚3𝑛5)
= 𝑚
−1
2
−3
𝑛
3
2
−5
= 𝑚−
1−6
2 𝑛
3−10
2
= 𝑚−
7
2𝑛−
7
2
=
1
𝑚
7
2𝑛
7
2
15. Determine the value of √50502 − 49502 is…
Solution :
√50502 − 49502
= √50502 – √49502
= 5050 – 4950
= 100

6. 16. Simplify the following questions.
Solution :
𝑎−
2
3
𝑎−
1
3
√𝑎2
3
=
𝑎−
2
3
𝑎−
1
3
𝑎
2
3
=
𝑎−
2
3
𝑎
1
3
= 𝑎
−2−1
3
= 𝑎−
3
3
= 𝑎−1
=
1
𝑎
17. In the form of a rational rank √𝑥3 √𝑥3
5
√𝑥3
3
is…
Solution :
√𝑥3 √𝑥3
5
√𝑥3
3
=
√
𝑥3 √𝑥3 × 𝑥
3
2
5
3
=
√
𝑥3 √𝑥3+
3
2
5
3
=
√
𝑥3 √𝑥
9
2
5
3
= √𝑥3𝑥
9×1
2×5
3
= √𝑥3𝑥
9
10
3
= √𝑥3+
9
10
3
= √𝑥
39
10
3
= 𝑥
39×1
10×3
= 𝑥
13
10

7. 18. Determine the value of √√𝑥2
4
6
is…
Solution :
√√𝑥2
4
6
= √𝑥2
6∙4
= √𝑥2
24
= 𝑥
2
24
= 𝑥
1
12
= √𝑥
12
19. Determine the value of √25𝑥
1
3
𝑥
1
5
4
is…
Solution :
√
25𝑥
1
3
𝑥
1
5
4
= √25𝑥
5−3
15
4
= √25𝑥
2
15
4
= 25
1
4𝑥
2×1
15×4
= 52×
1
4𝑥
2
60
= 5
1
2𝑥
1
30
20. Determine the value of (0,0001)−1
× √0,04 is…
Solution :
(0,0001)−1
× √0,04
= (10)−4×−1
× 0,2
= 104
× (2 × 10−1)
= 2 × 103
= 2000

8. DARTAR PUSTAKA
Cunayah dan Ronald Sitorus. 2004. Ringkasan Matematika untuk SMA/ MA. Bandung:
Yrama Widya.
Umi Salamah. 2012. Berlogika dengan Matematika. PT Tiga Serangkai Pustaka
Mandiri.
Rosihan Ari Y dan Indryastuti. 2014. Perspektif Matematika. PT Tiga Serangkai
Pustaka Mandiri.