Kumpulan Soal : Bilangan Pangkat (eksponen)

✍Kuis Matematika: Pangkat dan Eksponen

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Soal No. 1

Nilai dari \((-3)^5\) adalah ….

A. \(-15\) B. \(15\) C. \(-243\) D. \(243\) E. \(-423\)

Penyelesaian: Lihat/Tutup

\[\begin{align}(-3)^5 &= (-3).(-3).(-3).(-3).(-3) \\ &= -243 \end{align}\] Jawaban: C

Soal No. 2

\((-5).(-5).(-5).(-5)\) = ….

A. \((-5)^4\) B. \((-4)^5\) C. \(-5^4\) D. \(-4^5\) E. \(-20\)

Penyelesaian: Lihat/Tutup

\[\underbrace{(-5).(-5).(-5).(-5)}_{(-5)\,\text{sebanyak 4}}=(-5)^4\] Jawaban: A

Soal No. 3

Bentuk \(\dfrac{a^{-1}b^2}{c^{-3}}\) dapat dinyatakan dengan pangkat positif menjadi ….

A. \(\dfrac{ab^2}{c^2}\) B. \(\dfrac{ac^3}{b^2}\) C. \(ab^2c^3\) D. \(\dfrac{b^2c^3}{a}\) E. \(\dfrac{1}{ab^2c^3}\)

Penyelesaian: Lihat/Tutup

\[\ddfrac{a^{-1}b^2}{c^{-3}}=a^{-1}b^2c^3=\dfrac{b^2c^3}{a}\] Jawaban: D

Soal No. 4

Bentuk sederhana dari \(\dfrac{3^2x^4y^{-2}}{6^3x^2y^{-3}}\) adalah ….

A. \(\dfrac{1}{2}x^2y\) B. \(\dfrac{1}{18}x^2y\) C. \(\dfrac{1}{18}x^6y\) D. \(\dfrac{1}{24}x^2y\) E. \(\dfrac{1}{24}x^6y\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{3^2x^4y^{-2}}{6^3x^2y^{-3}} &= \dfrac{3^2x^4y^{-2}}{(2.3)^3x^2y^{-3}} \\ &= \dfrac{3^2x^4y^{-2}}{2^3.3^3x^2y^{-3}} \\ &= 2^{-3}{{.3}^{2-3}}{{x}^{4-2}}{{y}^{-2-(-3)}} \\ &= 2^{-3}{{.3}^{-1}}x^2{{y}^{1}} \\ &= \dfrac{1}{2^3.3}.x^2y \\ &= \dfrac{1}{24}x^2y \end{align}\] Jawaban: D

Soal No. 5

Bentuk sederhana dari \(\dfrac{{{(m^2)}^{-2}}n^2}{m^{-5}n^4}\) adalah ....

A. \(mn\) B. \(\dfrac{m}{n}\) C. \(\dfrac{n}{m}\) D. \(\dfrac{m^2}{n}\) E. \(m^2n\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(m^2)^{-2}n^2}{m^{-5}n^4} &= \dfrac{m^{2\times (-2)}n^2}{m^{-5}n^4} \\ &= \dfrac{{{m}^{-4}}n^2}{m^{-5}n^4} \\ &= {m^{-4-(-5)}}{n^{5-4}} \\ &= mn \end{align}\] Jawaban: A

Soal No. 6

Bentuk sederhana dari \(\left( \dfrac{2x^{-5}y^3}{4x^3y^{-2}} \right)^2\) adalah ….

A. \(\dfrac{y^{10}}{4x^{16}}\) B. \(\dfrac{y^2}{2x^{16}}\) C. \(\dfrac{y^2}{4x^4}\) D. \(\dfrac{y^{10}}{2x^{16}}\) E. \(\dfrac{y^2}{4x^{16}}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{2x^{-5}y^3}{4x^3y^{-2}} \right)^2 &= \dfrac{2^2x^{-5.2}y^{3.2}}{4^2x^{3.2}y^{-2.2}} \\ &= \dfrac{4x^{-10}y^6}{16x^6y^{-4}} \\ &= \dfrac{x^{-10-6}y^{6-(-4)}}{4} \\ &= \dfrac{x^{-16}y^{10}}{4} \\ &= \dfrac{y^{10}}{4x^{16}} \end{align}\] Jawaban: A

Soal No. 7

Bentuk sederhana dari \(\left( \dfrac{3x^{-2}y^3}{2x^{-3}y^2} \right)^2\) adalah ….

A. \(\dfrac{3y^2}{2x^2}\) B. \(\dfrac{3x^2}{2y^2}\) C. \(\dfrac{9}{4}x^2y^2\) D. \(\dfrac{9}{4}x^{-2}y^2\) E. \(\dfrac{9}{4}x^2y^{-2}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{3x^{-2}y^3}{2x^{-3}y^2} \right)^2 &= \dfrac{3^2x^{-2.2}y^{3.2}}{2^2x^{-3.2}y^{2.2}} \\ &= \dfrac{9x^{-4}y^6}{4x^{-6}y^4} \\ &= \dfrac{9}{4}x^{-4-(-6)}y^{6-4} \\ &= \dfrac{9}{4}x^2y^2 \end{align}\] Jawaban: C

Soal No. 8

Bentuk sederhana dari \(\left( \dfrac{3^{-1}a^3b^{-4}}{2a^{-2}b} \right)^{-1}\) adalah ….

A. \(\dfrac{2a^5}{3b^5}\) B. \(\dfrac{3a^5}{2b^5}\) C. \(\dfrac{a^5}{6b^5}\) D. \(\dfrac{6a^5}{b^5}\) E. \(\dfrac{6b^5}{a^5}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{3^{-1}a^3b^{-4}}{2a^{-2}b} \right)^{-1} &= \dfrac{2a^{-2}b}{3^{-1}a^3b^{-4}} \\ &= 2.3.a^{-2-3}b^{1-(-4)} \\ &= 6a^{-5}b^5 \\ &= \dfrac{6b^5}{a^5} \end{align}\] Jawaban: E

Soal No. 9

Bentuk sederhana dari \(\left( \dfrac{2a^5b^{-5}}{32a^9b^{-1}} \right)^{-1}\) adalah ….

A. \((2ab)^4\) B. \((2ab)^2\) C. \(2ab\) D. \((2ab)^{-1}\) E. \((2ab)^{-4}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{2a^5b^{-5}}{32a^9b^{-1}} \right)^{-1} &= \dfrac{32a^9b^{-1}}{2a^5b^{-5}} \\ &= \dfrac{2^5a^9b^{-1}}{2a^5b^{-5}} \\ &= 2^{5-1}a^{9-5}b^{-1-(-5)} \\ &= 2^4a^4b^4 \\ &= (2ab)^4 \end{align}\] Jawaban: A

Soal No. 10

Bentuk sederhana dari \({{\left( \dfrac{2x^2y^{-3}}{4xy^2} \right)}^{-2}}\) adalah ….

A. \(\dfrac{1}{xy}\) B. \(\dfrac{1}{2}xy\) C. \(x^2y^{10}\) D. \(4xy^2\) E. \(\dfrac{4y^{10}}{x^2}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{2x^2y^{-3}}{4xy^2} \right)^{-2} &= \left( \dfrac{4xy^2}{2x^2y^{-3}} \right)^2 \\ &= {\left( \dfrac{2xy^2}{x^2y^{-3}} \right)^{2}} \\ &= \dfrac{2^2x^2y^{2.2}}{x^{2.2}y^{-3.2}} \\ &= \dfrac{2^2x^2y^4}{x^4{{y}^{-6}}} \\ &= 4{{x}^{2-4}}{{y}^{4-(-6)}} \\ &= 4x^{-2}y^{10} \\ &= \dfrac{4y^{10}}{x^2} \end{align}\] Jawaban: E

Soal No. 11

Bentuk sederhana dari \(\left( \dfrac{2x^5y^{-4}}{5x^8y^{-6}} \right)^{-3}\) adalah ….

A. \(\dfrac{8x^3}{125y}\) B. \(\dfrac{8x^9}{125y^6}\) C. \(\dfrac{16y^6}{625x^9}\) D. \(\dfrac{125x^9}{8y^6}\) E. \(\dfrac{625x^9}{125y^6}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{2x^5y^{-4}}{5x^8y^{-6}} \right)^{-3} &= \left( \dfrac{5x^8y^{-6}}{2x^5y^{-4}} \right)^3 \\ &= \dfrac{5^3x^{8.3}y^{-6.3}}{2^3x^{5.3}y^{-4.3}} \\ &= \dfrac{125x^{24}y^{-18}}{8x^{15}y^{-12}} \\ &= \dfrac{125x^{24-15}y^{-18-(-12)}}{8} \\ &= \dfrac{125x^9y^{-6}}{8} \\ &= \dfrac{125x^9}{8y^6} \end{align}\] Jawaban: D

Soal No. 12

Bentuk sederhana dari \((6^{-2}a^2)^3:(12^3a^3)^{-2}\) adalah ….

A. \(2^{-1}\) B. 2 C. \(2a^{12}\) D. \(2^6a^{12}\) E. \(2^{-6}a^{-12}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}(6^{-2}a^2)^3:(12^3a^3)^{-2} &= \dfrac{(6^{-2}a^2)^3}{(12^3a^3)^{-2}} \\ &= \dfrac{6^{-2.3}a^{2.3}}{12^{3.(-2)}a^{3.(-2)}} \\ &= \dfrac{6^{-6}a^6}{12^{-6}a^{-6}} \\ &= \dfrac{6^{-6}a^{6-(-6)}}{(2.6)^{-6}} \\ &= \dfrac{6^{-6}a^{12}}{2^{-6}.6^{-6}} \\ &= 2^6a^{12} \end{align}\] Jawaban: D

Soal No. 13

Jika \(a\ne 0\) dan \(b\ne 0\) maka bentuk \(\dfrac{(8a^3b^4)^2}{(2a^{-1}b^2)^3}\) = ….

A. \(4a^8b^{14}\) B. \(4a^8b^2\) C. \(4a^9b^{14}\) D. \(4a^9b^{14}\) E. \(8a^9b^2\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(8a^3b^4)^2}{(2a^{-1}b^2)^3} &= \dfrac{{{(2^3a^3b^4)}^{2}}}{(2a^{-1}b^2)^3} \\ &= \dfrac{2^{3.2}a^{3.2}b^{4.2}}{2^3a^{-1.3}b^{2.3}} \\ &= \dfrac{2^6a^6b^8}{2^3a^{-3}b^6} \\ &= 2^{6-3}a^{6-(-3)}b^{8-6} \\ &= 2^3a^9b^2 \\ &= 8a^9b^2 \end{align}\] Jawaban: E

Soal No. 14

Bentuk sederhana dari \(\dfrac{\left( 3p^{-3}q^2 \right)^{-2}}{\left( pq^{-3} \right)^3}\) adalah ….

A. \(\dfrac{1}{9}p^5q^3\) B. \(9p^5q^3\) C. \(3p^3q^5\) D. \(9p^3q^5\) E. \(\dfrac{1}{9}p^3q^5\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(3p^{-3}q^2)^{-2}}{(pq^{-3})^3} &= \dfrac{3^{-2}p^{-3.(-2)}q^{2.(-2)}}{p^3q^{-3.3}} \\ &= \dfrac{3^{-2}p^6q^{-4}}{p^3q^{-9}} \\ &= 3^{-2}p^{6-3}q^{-4-(-9)} \\ &= \dfrac{1}{3^2}.p^3q^5 \\ &= \dfrac{1}{9}p^3q^5 \end{align}\] Jawaban: E

Soal No. 15

Jika \(a\ne 0\) dan \(b\ne 0\) maka bentuk sederhana dari \(\dfrac{(2a^{-1}b^3)^2}{(3a^{-2}b^4)^{-1}}\) adalah ….

A. \(12a^{-4}b^{10}\) B. \(12a^4b^{-10}\) C. \(\dfrac{2}{3}a^{-4}b^{-8}\) D. \(\dfrac{1}{3}ab^{10}\) E. \(\dfrac{1}{4}a^{-4}b^8\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(2a^{-1}b^3)^2}{(3a^{-2}b^4)^{-1}} &= \dfrac{2^2a^{-1.2}b^{3.2}}{3^{-1}a^{-2.(-1)}b^{4.(-1)}} \\ &= \dfrac{2^2a^{-2}b^6}{3^{-1}a^2b^{-4}} \\ &= 2^2.3.a^{-2-2}b^{6-(-4)} \\ &= 12a^{-4}b^{10} \end{align}\] Jawaban: A

Soal No. 16

Bentuk sederhana dari \(\dfrac{{{(4p^2q^3)}^{-1}}}{{{(2p^{-1}q^{-4})}^{-2}}}\) adalah ….

A. \(\dfrac{1}{p^4q^{11}}\) B. \(\dfrac{1}{4}p^4q^{-11}\) C. \(\dfrac{1}{4}p^{-4}q^{-11}\) D. \(p^4q^{11}\) E. \(p^{-4}q^{11}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(4p^2q^3)^{-1}}{(2p^{-1}q^{-4})^{-2}} &= \dfrac{4^{-1}p^{2.(-1)}q^{3.(-1)}}{2^{-2}p^{-1.(-2)}q^{-4.(-2)}} \\ &= \dfrac{4^{-1}p^{-2}q^{-3}}{2^{-2}p^2q^8} \\ &= 4^{-1}.2^2p^{-2-2}q^{-3-8} \\ &= 4^{-1}.4p^{-4}q^{-11} \\ &= \dfrac{4}{4p^4q^{11}} \\ &= \dfrac{1}{p^4q^{11}} \end{align}\] Jawaban: A

Soal No. 17

Diketahui \(a=\dfrac{1}{2}\), \(b=2\) dan \(c=1\). Nilai dari \(\dfrac{a^{-2}bc^3}{ab^2{{c}^{-1}}}\) adalah ….

A. 1 B. 4 C. 16 D. 64 E. 96

Penyelesaian: Lihat/Tutup

\(a=\dfrac{1}{2}\Leftrightarrow a=2^{-1}\), \(b=2\) dan \(c=1\) maka:
\[\begin{align}\dfrac{a^{-2}bc^3}{ab^2c^{-1}} &= \dfrac{(2^{-1})^{-2}.2.1^3}{2^{-1}.2^2.1^{-1}} \\ &= \dfrac{2^{-1.(-2)}.2}{2^{-1+2}} \\ &= \dfrac{2^2.2}{2} \\ &= 4 \end{align}\] Jawaban: B

Soal No. 18

Diketahui \(a=4\), \(b=2\) dan \(c=\dfrac{1}{2}\). Nilai \({{(a^{-1})}^2}\times \dfrac{b^4}{c^{-3}}\) = ….

A. \(\dfrac{1}{2}\) B. \(\dfrac{1}{4}\) C. \(\dfrac{1}{8}\) D. \(\dfrac{1}{16}\) E. \(\dfrac{1}{32}\)

Penyelesaian: Lihat/Tutup

\(a=4\Leftrightarrow a=2^2\), \(b=2\) dan \(c=\dfrac{1}{2}\Leftrightarrow c=2^{-1}\)
\[\begin{align}(a^{-1})^2\times \dfrac{b^4}{c^{-3}} &= a^{-2}\times \dfrac{b^4}{c^{-3}} \\ &= (2^2)^{-2}\times \dfrac{2^4}{(2^{-1})^{-3}} \\ &= \dfrac{2^{-4+4}}{2^3} \\ &= \dfrac{2^0}{2^3} \\ &= \dfrac{1}{8} \end{align}\] Jawaban: C

Soal No. 19

Nilai dari \(\dfrac{a^2b^3c^{-1}}{a^{-2}bc^2}\) untuk \(a=2\), \(b=3\) dan \(c=5\) adalah ….

A. \(\dfrac{81}{125}\) B. \(\dfrac{144}{125}\) C. \(\dfrac{432}{125}\) D. \(\dfrac{1296}{125}\) E. \(\dfrac{2596}{125}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{a^2b^3c^{-1}}{a^{-2}bc^2} &= a^{2-(-2)}b^{3-1}c^{-1-2} \\ &= a^4b^2c^{-3} \\ &= \dfrac{a^4b^2}{c^3} \\ &= \dfrac{2^4.3^2}{5^3} \\ &= \dfrac{144}{125} \end{align}\] Jawaban: B

Soal No. 20

Jika diketahui \(x=\dfrac{1}{3}\), \(y=\dfrac{1}{5}\) dan \(z=2\) maka nilai dari \(\dfrac{x^{-4}yz^{-2}}{x^{-3}y^2z^{-4}}\) adalah ….

A. 32 B. 60 C. 100 D. 320 E. 640

Penyelesaian: Lihat/Tutup

\(x=\dfrac{1}{3}\Leftrightarrow x=3^{-1}\), \(y=\dfrac{1}{5}\Leftrightarrow y={{5}^{-1}}\) dan \(z=2\) maka:
\[\begin{align}\dfrac{x^{-4}yz^{-2}}{x^{-3}y^2z^{-4}} &= x^{-4-(-3)}y^{1-2}z^{-2-(-4)} \\ &= x^{-1}y^{-1}z^2 \\ &= (3^{-1})^{-1}.(5^{-1})^{-1}.2^2 \\ &= 3.5.4 \\ &= 60 \end{align}\] Jawaban: B

Soal No. 21

Bentuk sederhana dari \(\dfrac{16x^2y^{-3}}{2x^{-4}y^{-7}}\) adalah ….

A. \(2x^{-6}y^{-10}\) B. \(2^3x^6y^4\) C. \(2{x^{\dfrac{1}{2}}}{y^{\dfrac{3}{7}}}\) D. \(2{x^{-\dfrac{1}{2}}}{y^{\dfrac{3}{7}}}\) E. \(2{x^{\dfrac{1}{2}}}{y^{-\dfrac{3}{7}}}\)

Penyelesaian: Lihat/Tutup

\[\dfrac{16x^2y^{-3}}{2x^{-4}y^{-7}}=8{x^{2-(-4)}}{y^{-3-(-7)}}=2^3x^6y^4\] Jawaban: B

Soal No. 22

Bentuk sederhana dari \(\dfrac{7x^3y^{-4}{z^{-6}}}{84{x^{-7}}{y^{-1}}z^{-4}}\) = ….

A. \(\dfrac{{x^{10}}{z^{10}}}{12y^3}\) B. \(\dfrac{{z^2}}{12x^4y^3}\) C. \(\dfrac{{x^{10}}{y^{5}}}{12{z^2}}\) D. \(\dfrac{y^3{z^2}}{12x^4}\) E. \(\dfrac{{x^{10}}}{12y^3{z^2}}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{7x^3y^{-4}z^{-6}}{84x^{-7}y^{-1}z^{-4}} &= \dfrac{x^{3-(-7)}y^{-4-(-1)}z^{-6-(-4)}}{12} \\ &= \dfrac{x^{10}y^{-3}z^{-2}}{12} \\ &= \dfrac{x^{10}}{12y^3z^2} \end{align}\] Jawaban: E

Soal No. 23

Bentuk sederhana dari \(\dfrac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}}\) = ….

A. \(\dfrac{4c^5}{a^3b^5}\) B. \(\dfrac{4b}{a^5c^5}\) C. \(\dfrac{4b}{a^3c}\) D. \(\dfrac{4bc^7}{a^5}\) E. \(\dfrac{4c^7}{a^3b}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}} &= 4a^{-7-(-2)}b^{-2-(-3)}c^{1-(-6)} \\ &= 4a^{-5}b^{1}c^7 \\ &= \dfrac{4bc^7}{a^5} \end{align}\] Jawaban: D

Soal No. 24

Bentuk sederhana dari \(\left( \dfrac{27a^{-5}b^{-3}}{3^5a^{-7}b^{-5}} \right)^{-1}\) = ….

A. \((3ab)^2\) B. \(3(ab)^2\) C. \(9(ab)^2\) D. \(\dfrac{3}{(ab)^2}\) E. \(\dfrac{9}{(ab)^2}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{27a^{-5}b^{-3}}{3^5a^{-7}b^{-5}} \right)^{-1} &= \dfrac{3^5a^{-7}b^{-5}}{27a^{-5}b^{-3}} \\ &= \dfrac{3^5a^{-7}b^{-5}}{3^3a^{-5}b^{-3}} \\ &= 3^{5-3}a^{-7-(-5)}b^{-5-(-3)} \\ &= 3^2a^{-2}b^{-2} \\ &= \dfrac{9}{a^2b^2} \\ &= \dfrac{9}{(ab)^2} \end{align}\] Jawaban: E

Soal No. 25

Bentuk sederhana dari \(\dfrac{(5a^3b^{-2})^4}{(5a^4b^{-5})^{-2}}\) adalah ….

A. \(5^6a^4{{b}^{-18}}\) B. \(5^6a^4b^2\) C. \(5^2a^4b^2\) D. \(5^6ab^{-1}\) E. \(5^6a^9b^{-1}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(5a^3b^{-2})^4}{(5a^4b^{-5})^{-2}} &= \dfrac{5^4a^{3.4}b^{-2.4}}{5^{-2}a^{-4.(-2)}b^{-5.(-2)}} \\ &= \dfrac{5^4a^{12}b^{-8}}{5^{-2}a^8b^{10}} \\ &= 5^{4-(-2)}a^{12-8}b^{-8-10} \\ &= 5^6a^4b^{-18} \end{align}\] Jawaban: A

Soal No. 26

Bentuk sederhana dari \(\dfrac{36x^2y^2}{15ab}.\dfrac{5b(ab)^2}{24x^3y^2}\) adalah ….

A. \(\dfrac{5a}{2x}\) B. \(\dfrac{ab^2}{2x}\) C. \(\dfrac{ay}{2x}\) D. \(\dfrac{ab}{2y}\) E. \(\dfrac{3b}{2x}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{36x^2y^2}{15ab}.\dfrac{5b(ab)^2}{24x^3y^2} &= \dfrac{x^2y^2}{ab}.\dfrac{ba^2b^2}{2x^3y^2} \\ &= \dfrac{x^{2-3}y^{2-2}a^{2-1}b^{1+2-1}}{2} \\ &= \dfrac{x^{-1}ab^2}{2} \\ &= \dfrac{ab^2}{2x} \end{align}\] Jawaban: B

Soal No. 27

Bentuk \(\dfrac{{{(2x^3y^{-4})}^{-3}}}{4x^{-4}y^2}\) dapat disederhanakan menjadi ….

A. \({\left( \dfrac{y^2}{2x} \right)^{5}}\) B. \({\left( \dfrac{2y^2}{x} \right)^{5}}\) C. \(\dfrac{1}{2}{\left( \dfrac{y^2}{x} \right)^{5}}\) D. \(\dfrac{y^{10}}{32x^5}\) E. \(\dfrac{{y^{14}}}{2x^5}\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{(2x^3y^{-4})^{-3}}{4x^{-4}y^2} &= \dfrac{2^{-3}x^{3.(-3)}y^{-4.(-3)}}{2^2x^{-4}y^2} \\ &= \dfrac{2^{-3}x^{-9}y^{12}}{2^2x^{-4}y^2} \\ &= 2^{-3-2}x^{-9-(-4)}y^{12-2} \\ &= 2^{-5}x^{-5}y^{10} \\ &= \dfrac{y^{10}}{2^5x^5} \\ &= \dfrac{y^{2.5}}{2^5x^5} \\ &= \left( \dfrac{y^2}{2x} \right)^5 \end{align}\] Jawaban: A

Soal No. 28

Hasil dari \(\left( \dfrac{2a^2}{c^{-1}} \right)^4.\dfrac{b}{a^2}:8a^6c^3\) = ….

A. \(\dfrac{a^{10}b}{c}\) B. \(\dfrac{b}{a^2c}\) C. \(\dfrac{2a^8b}{c}\) D. \(2bc\) E. \(2a^{10}bc\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\left( \dfrac{2a^2}{c^{-1}} \right)^4.\dfrac{b}{a^2}\div 8a^6c^3 &= \dfrac{2^4a^{2.4}}{c^{-1.4}}.\dfrac{b}{a^2}.\dfrac{1}{8a^6c^3} \\ &= \dfrac{2^4a^8}{c^{-4}}.\dfrac{b}{a^2}.\dfrac{1}{2^3a^6c^3} \\ &= 2^{4-3}a^{8-2-6}bc^{4-3} \\ &= 2bc \end{align}\] Jawaban: D

Soal No. 29

Bentuk sederhana dari \({\left( \dfrac{1}{1+p} \right)^{5}}{\left( \dfrac{1}{1-p} \right)^{-7}}{\left( \dfrac{p-1}{1+p} \right)^{-6}}\) = ….

A. \(p\) B. \(1-p^2\) C. \(p^2-1\) D. \(p^2+2p+1\) E. \(p^2-2p+1\)

Penyelesaian: Lihat/Tutup

\({\left( \dfrac{1}{1+p} \right)^{5}}{\left( \dfrac{1}{1-p} \right)^{-7}}{\left( \dfrac{p-1}{1+p} \right)^{-6}}\)
= \(\dfrac{1}{(1+p)^5}.(1-p)^7.{\left( \dfrac{1+p}{p-1} \right)^{6}}\)
= \((1+p)^{-5}.(1-p)^7.\dfrac{(1+p)^6}{(1-p)^6}\)
= \((1+p)^{-5+6}.(1-p)^{7-6}\)
= \((1+p)(1-p)\)
= \(1-p^2\)
Jawaban: B

Soal No. 30

Bentuk \(\dfrac{a^{-1}+b^{-1}}{ab}\) dapat dinyatakan dengan bentuk ….

A. \(\dfrac{a+b}{ab}\) B. \(\dfrac{a+b}{a^2b^2}\) C. \(\dfrac{1}{a^2b^2}\) D. \(\dfrac{1}{a+b}\) E. \(a+b\)

Penyelesaian: Lihat/Tutup

\[\begin{align}\dfrac{a^{-1}+b^{-1}}{ab} &= \dfrac{\dfrac{1}{a}+\dfrac{1}{b}}{ab} \\ &= \dfrac{\dfrac{b+a}{ab}}{ab} \\ &= \dfrac{a+b}{ab}\times \dfrac{1}{ab} \\ &= \dfrac{a+b}{a^2b^2} \end{align}\] Jawaban: B