HALOO MINTA TOLONG BANTU JAWAB DONG KAK BESOK MAU DIKUMPUL NO NGASAL YA KAK, SAMA TOLONG PAKAI CARA YAA
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Jawab:
Penjelasan dengan langkah-langkah:
Soal No. 1a
[tex]=3^{5}*9^{7}*27^{3}\\\\=3^{5}*(3^{2})^{7}*(3^{3})^{3}\\\\=3^{5}*3^{(2*7)}*3^{(3*3)}\\\\=3^{5}*3^{14}*3^{9}\\\\=3^{5+14+9}\\\\=3^{28}[/tex]
Soal No. 1b
[tex]=2^{3}*3^{6}*24^{5}\\\\=2^{3}*3^{6}*(2^{3}*3)^{5}\\\\=2^{3}*3^{6}*(2^{3})^{5}*3^{5}\\\\=2^{3}*3^{6}*2^{(3*5)}*3^{5}\\\\=2^{3}*3^{6}*2^{15}*3^{5}\\\\=2^{(3+15)}*3^{(6+5)}\\\\=2^{18}*3^{11}[/tex]
Soal No. 2
[tex]=(-3)^{3}*(\frac{1}{15})^{3}*(\frac{10}{9})^{4}*(\frac{27}{25})^{5}\\\\=(-3)^{3}*(\frac{1}{3*5})^{3}*(\frac{2*5}{3^{2}})^{4}*(\frac{3^{3}}{5^{2}})^{5}\\\\=(-3)^{3}*\frac{1}{3^{3}*5^{3}}*\frac{2^{4}*5^{4}}{(3^{2})^{4}}*\frac{(3^{3})^{5}}{(5^{2})^{5}}\\\\=(-3)^{3}*\frac{1}{3^{3}*5^{3}}*\frac{2^{4}*5^{4}}{3^{8}}*\frac{3^{15}}{5^{10}}\\\\=(-3)^{3}*3^{-3}*5^{-3}*2^{4}*5^{4}*3^{-8}*3^{15}*5^{-10}\\\\=(-3)^{3}*3^{(-3-8+15)}*5^{(-3+4-10)}*2^{4}\\\\=(-3)^{3}*3^{4}*5^{(-9)}*2^{4}\\[/tex]
Soal No 3a
[tex]=(\frac{2^{6}*a^{5}*b^{7}*c^{-3}}{2^{12}*a^{-2}*b^{-4}*c^{6}})^{-4}\\\\=\frac{2^{(6*(-4))}*a^{(5*(-4))}*b^{(7*(-4))}*c^{((-3)*(-4))}}{2^{(12*(-4))}*a^{((-2)*(-4))}*b^{((-4)*(-4))}*c^{(6*(-4))}}\\\\=\frac{2^{(-24)}*a^{(-20)}*b^{(-28)}*c^{12}}{2^{(-48)}*a^{(8)}*b^{(16)}*c^{(-24)}}\\\\=\frac{2^{(48)}*c^{(24)}*c^{12}}{2^{(24)}*a^{(8)}*a^{(20)}*b^{(16)}*b^{(28)}}\\\\=\frac{2^{24}*c^{36}}{a^{28}*b^{44}}\\\\[/tex]
Soal No 3b
[tex]=(\frac{3*p^{6}*q^{5}}{81*p^{4}*q^{2}})^{(-1)}\\\\=(\frac{3*p^{6}*q^{5}}{3^{4}*p^{4}*q^{2}})^{(-1)}\\\\=\frac{3^{(-1)}*p^{(6*(-1))}*q^{(5*(-1))}}{3^{(4*(-1))}*p^{(4*(-1))}*q^{(2*(-1))}}\\\\=\frac{3^{(-1)}*p^{(-6)}*q^{(-5)}}{3^{(-4))}*p^{(-4)}*q^{(-2)}}\\\\=3^{(-1)}*3^{4}*p^{(-6)}*p^{4}*q^{(-5)}}{*q^{2}}\\\\=3^{((-1)+4)}*p^{((-6)+4)}*q^{((-5)+2)}\\\\=3^{3}*p^{(-2)}*q^{(-3)}\\\\=\frac{3^{3}}{p^{2}*q^{3}}\\\\=\frac{27}{p^{2}*q^{3}}[/tex]