SOAL A.
[tex]{12}^{6} \times {36}^{8} \times{( \frac{2}{3})}^{ - 5} [/tex]
[tex] = {12}^{6} \times {36}^{8} \times {( \frac{3}{2})}^{5} [/tex]
[tex] = {(3 \times 4)}^{6} \times {(4 \times 9)}^{8} \times {( \frac{3}{2})}^{5} [/tex]
[tex] = {3}^{6} \times {4}^{6} \times {4}^{8} \times {9}^{8} \times \frac{ {3}^{5} }{ {2}^{5} } [/tex]
[tex] = {3}^{6} \times {({2}^{2})}^{6} \times{({2}^{2})}^{8} \times{({3}^{2})}^{8} \times \frac{ {3}^{5} }{ {2}^{5} } [/tex]
[tex] = \frac{ {3}^{6} \times {2}^{2 \times 6} \times {2}^{2 \times 8} \times {3}^{2 \times 8} \times {3}^{5} }{ {2}^{5} } [/tex]
[tex] = \frac{ {3}^{6} \times {2}^{12} \times {2}^{16} \times {3}^{16} \times {3}^{5} }{ {2}^{5} } [/tex]
[tex] = {2}^{12 + 16 - 5} \times {3}^{6 + 16 + 5} [/tex]
[tex] = {2}^{23} \times {3}^{27} [/tex]
SOAL B.
[tex] \frac{ {3}^{10} \times {9}^{ - 3}}{ { - 81}^{2} \times {( - 27)}^{ - 4} } [/tex]
INGAT :
Bilangan pokok negatif yang dipangkatkan dengan pangkat bilangan genap sama dengan positif.
[tex] = - \frac{ {3}^{10} \times {9}^{ - 3}}{ { 81}^{2} \times {27}^{ - 4} } [/tex]
[tex] = - \frac{ {3}^{10} \times {({3}^{2})}^{ - 3}}{ {({3}^{4})}^{2} \times {({3}^{3})}^{ - 4} } [/tex]
[tex] = - \frac{ {3}^{10} \times {3}^{2 \times ( - 3)}}{ {3}^{4 \times 2} \times {3}^{3 \times ( - 4)} } [/tex]
[tex] = - \frac{{3}^{10} \times {3}^{ - 6}}{ {3}^{8} \times {3}^{ - 12} } [/tex]
[tex] = - \frac{ {3}^{10 + ( - 6)} }{ {3}^{8 + ( - 12)} }[/tex] [tex] = - \frac{ {3}^{4} }{ {3}^{ - 4} } = - {3}^{4 - ( - 4)} = - {3}^{8} [/tex]
SOAL C.
[tex] \frac{ {5}^{12} \div {5}^{4}}{ {( - 5)}^{3} \times {( \frac{1}{125})}^{2} } [/tex]
INGAT :
Bilangan pokok negatif yang dipangkatkan dengan pangkat bilangan ganjil sama dengan negatif.
[tex] = - \frac{ {5}^{12} \div {5}^{4} }{ {5}^{3} \times {( \frac{1}{125})}^{2} } [/tex]
[tex] = - \frac{ {5}^{12} \div {5}^{4} }{ {5}^{3} \times {( \frac{1}{ {5}^{3} })}^{2} } [/tex]
[tex] = - \frac{ {5}^{12 - 4} }{ {5}^{3} \times \frac{1}{ {5}^{3 \times 2} } } [/tex]
[tex] = - \frac{ {5}^{8} }{ {5}^{3} \times \frac{1}{ {5}^{6} } } [/tex]
[tex] = - \frac{ {5}^{8} }{( \frac{ {5}^{3} }{ {5}^{6} } )} [/tex] [tex] = - \frac{ {5}^{8} }{ {5}^{3 - 6} } = - \frac{ {5}^{8} }{ {5}^{ - 3} } = - {5}^{8 - ( - 3)} = - {5}^{11} [/tex]
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