Exercise Zone : Pangkat (Eksponen) [3]

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Berikut ini adalah kumpulan soal mengenai Pangkat. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

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No. 21

Hasil dari (2³)² ⋅ (2³)⁻³ adalah ....

1. 8
2. −8
3. ${\displaystyle \frac{1}{8}}$

4. 6
5. −6

UKK 2022 Kelas X

ALTERNATIF PENYELESAIAN

CARA 1

$$\begin{array}{rl}{\left(2^3\right)}^2\cdot {\left(2^3\right)}^{-3}& =\left(2^6\right)\cdot \left(2^{-9}\right)\\ & =2^{6+(-9)}\\ & =2^{-3}\\ & ={\displaystyle \frac{1}{2^3}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{1}{8}}}}}}\end{array}$$

CARA 2

$$\begin{array}{rl}{\left(2^3\right)}^2\cdot {\left(2^3\right)}^{-3}& ={\left(2^3\right)}^{2+(-3)}\\ & ={\left(2^3\right)}^{-1}\\ & ={\displaystyle \frac{1}{2^3}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{1}{8}}}}}}\end{array}$$

Jadi, hasil dari (2³)² ⋅ (2³)⁻³ adalah ${\displaystyle \frac{1}{8}}$.
JAWAB: C

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No. 22

Hasil dari ${\displaystyle \frac{2^{10}\cdot 2^5}{2^{12}}}$ adalah ....

1. 2
2. 4
3. 8

4. 12
5. 16

UKK 2022 Kelas X

ALTERNATIF PENYELESAIAN

$$\begin{array}{rl}{\displaystyle \frac{2^{10}\cdot 2^5}{2^{12}}}& =2^{10+5-12}\\ & =2^3\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 8}}}}\end{array}$$

Jadi, hasil dari ${\displaystyle \frac{2^{10}\cdot 2^5}{2^{12}}}$ adalah 8.
JAWAB: C

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No. 23

Bentuk sederhana dari $2^3\times3^2\times4^{\frac12}$ adalah ....

1. 106
2. 144

3. 114
4. 136

5. 141

USP 2024 Kurikulum Merdeka

ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{2}^3\times 3^2\times 4^{\frac{1}{2}}& =8\times 9\times {\left(2^2\right)}^{\frac{1}{2}}\\ & =72\times 2\\ & =\text{color}blue\boxed{{\displaystyle \boxed{{\displaystyle \text{color}black144}}}}\end{array}$

Jadi, bentuk sederhana dari $2^3\times3^2\times4^{\frac12}$ adalah 144.
JAWAB: B

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No. 24

Sederhanakanlah $${\left({\displaystyle \frac{2^4\times 3^6}{2^3\times 3^2}}\right)}^3$$

Buku Siswa Kelas X Kurikulum Merdeka

ALTERNATIF PENYELESAIAN

$$\begin{array}{rl}{\left({\displaystyle \frac{2^4\times 3^6}{2^3\times 3^2}}\right)}^3& ={(2^{4-3}\times 3^{6-2})}^3\\ & ={(2\times 3^4)}^3\\ & =2^3\times 3^{4\times 3}\\ & =2^3\times 3^{12}\end{array}$$

Jadi, $\left(\dfrac{2^4\times3^6}{2^3\times3^2}\right)^3=2^3\times3^{12}.$

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No. 25

Bentuk sederhana dari (a²b)³⋅(a²b⁴)⁻¹ adalah ....

1. ${\displaystyle \frac{a^5}{b}}$
2. ${\displaystyle \frac{a^4}{b}}$
3. a³b

4. a²b²
5. ab³

UN-TEK-06-01

ALTERNATIF PENYELESAIAN

$$\begin{array}{rl}{\left(a^{2}b\right)}^3\cdot {\left(a^2{b}^4\right)}^{-1}& =a^6{b}^3\cdot a^{-2}{b}^{-4}\\ & =a^{6-2}{b}^{3-4}\\ & =a^4{b}^{-1}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{a^4}{b}}}}}}\end{array}$$

Jadi, entuk sederhana dari (a²b)³⋅(a²b⁴)⁻¹ adalah ${\displaystyle \frac{a^4}{b}}$.

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JAWAB: B

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No. 26

4⁴ + 4⁴ + 4⁴ + 4⁴ = ....

1. 2⁷
2. 2¹⁰
3. 1034

4. 5⁴
5. 512

OSK SMP 2003

ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{4}^4+4^4+4^4+4^4& =4\cdot 4^4\\ & =4^5\\ & ={\left(2^2\right)}^5\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 2^{10}}}}}\end{array}$

Jadi, 4⁴ + 4⁴ + 4⁴ + 4⁴ = 2¹⁰.
JAWAB: B

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No. 27

Bentuk sederhana dari ${\displaystyle \frac{2a^3{b}^{-5}{c}^2}{6a^9{b}^2{c}^{-1}}}$ adalah ....

1. ${\displaystyle \frac{1}{3}}\left(a^6{b}^7{c}^3\right)$
2. ${\displaystyle \frac{1}{3}}\left(a^6{b}^{5}c\right)$
3. ${\displaystyle \frac{1}{3}}\left(b^{4}c\right)$

4. ${\displaystyle \frac{a{c}^3}{3b^7}}$
5. ${\displaystyle \frac{c^3}{3a^6{b}^7}}$

USP 2023

ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{\displaystyle \frac{2a^3{b}^{-5}{c}^2}{6a^9{b}^2{c}^{-1}}}& ={\displaystyle \frac{c^{2-(-1)}}{3a^{9-3}{b}^{2-(-5)}}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{c^3}{3a^6{b}^7}}}}}}\end{array}$

Jadi, bentuk sederhana dari ${\displaystyle \frac{2a^3{b}^{-5}{c}^2}{6a^9{b}^2{c}^{-1}}}$ adalah ${\displaystyle \frac{c^3}{3a^6{b}^7}}$.
JAWAB: E

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No. 28

Diketahui $a=\dfrac18$, b = 16 dan c = 4, maka nilai $a^{-1\frac13}\cdot b^{\frac14}\cdot c^{-1\frac12}$ adalah ....

1. $\dfrac1{256}$
2. $\dfrac14$
3. 1

4. 4
5. 256

Big Book Matematika SMA

ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{a}^{-1\frac{1}{3}}\cdot b^{\frac{1}{4}}\cdot c^{-1\frac{1}{2}}& ={\left({\displaystyle \frac{1}{8}}\right)}^{-\frac{4}{3}}\cdot {16}^{\frac{1}{4}}\cdot 4^{-\frac{3}{2}}\\ & ={\left({\displaystyle \frac{1}{2^3}}\right)}^{-\frac{4}{3}}\cdot {\left(2^4\right)}^{\frac{1}{4}}\cdot {\left(2^2\right)}^{-\frac{3}{2}}\\ & ={\left(2^{-3}\right)}^{-\frac{4}{3}}\cdot 2\cdot 2^{-3}\\ & =2^4\cdot 2\cdot 2^{-3}\\ & =2^2\\ & =\text{color}blue\boxed{{\displaystyle \boxed{{\displaystyle \text{color}black4}}}}\end{array}$

Jadi, $a^{-1\frac13}\cdot b^{\frac14}\cdot c^{-1\frac12}=4$.
JAWAB: D

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No. 29

Bentuk sederhana dari $\dfrac{3^{\frac56}\cdot12^{\frac7{12}}}{6^{\frac23}\cdot2^{-\frac14}}$ adalah ....

1. $6^{\frac14}$
2. $6^{\frac34}$
3. $6^{\frac32}$

4. $\left(\dfrac23\right)^{\frac34}$
5. $\left(\dfrac32\right)^{\frac34}$

Big Book Matematika SMA

ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{\displaystyle \frac{3^{\frac{5}{6}}\cdot {12}^{\frac{7}{12}}}{6^{\frac{2}{3}}\cdot 2^{-\frac{1}{4}}}}& ={\displaystyle \frac{3^{\frac{5}{6}}\cdot {(3\cdot 2^2)}^{\frac{7}{12}}}{(3\cdot 2{)}^{\frac{2}{3}}\cdot 2^{-\frac{1}{4}}}}\\ & ={\displaystyle \frac{3^{\frac{5}{6}}\cdot 3^{\frac{7}{12}}\cdot 2^{\frac{7}{6}}}{3^{\frac{2}{3}}\cdot 2^{\frac{2}{3}}\cdot 2^{-\frac{1}{4}}}}\\ & =3^{\frac{5}{6}+\frac{7}{12}-\frac{2}{3}}\cdot 2^{\frac{7}{6}-\frac{2}{3}-(-\frac{1}{4})}\\ & =3^{\frac{10}{12}+\frac{7}{12}-\frac{8}{12}}\cdot 2^{\frac{14}{12}-\frac{8}{12}+\frac{3}{12}}\\ & =3^{\frac{9}{12}}\cdot 2^{\frac{9}{12}}\\ & =3^{\frac{3}{4}}\cdot 2^{\frac{3}{4}}\\ & =(3\cdot 2{)}^{\frac{3}{4}}\\ & =\text{color}blue\boxed{{\displaystyle \boxed{{\displaystyle \text{color}black{6}^{\frac{3}{4}}}}}}\end{array}$

Jadi, bentuk sederhana dari $\dfrac{3^{\frac56}\cdot12^{\frac7{12}}}{6^{\frac23}\cdot2^{-\frac14}}$ adalah $6^{\frac34}$.
JAWAB: B

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No. 30

Bentuk sederhana dari $\dfrac{x^{-3}\cdot y^{-1}\cdot z^6}{x^{-5}\cdot y^4\cdot z^3}$ adalah ....

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ALTERNATIF PENYELESAIAN

$\begin{array}{rl}{\displaystyle \frac{x^{-3}\cdot y^{-1}\cdot z^6}{x^{-5}\cdot y^4\cdot z^3}}& ={\displaystyle \frac{x^{-3-(-5)}\cdot z^{6-3}}{y^{4-(-1)}}}\\ & =\text{color}blue\boxed{{\displaystyle \boxed{{\displaystyle \text{color}black{\displaystyle \frac{x^2\cdot z^3}{y^5}}}}}}\end{array}$

Jadi, bentuk sederhana dari $\dfrac{x^{-3}\cdot y^{-1}\cdot z^6}{x^{-5}\cdot y^4\cdot z^3}$ adalah $\dfrac{x^2\cdot z^3}{y^5}$.

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