a. 2⁷ x 6⁷
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4⁷
b. 6⁷ x 3³
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2⁷
c. 21⁵ (7)²
__ : __
9² (2)
SOAL A.
[tex] \frac{ {( - 4)}^{5} }{ {( - 4)}^{2} } = {( - 4)}^{5 - 2} = {( - 4)}^{3} [/tex]
SOAL B.
[tex] \frac{ {( - 4)}^{6} }{ {( - 4)}^{2} } = {( - 4)}^{6 - 2} = {( - 4)}^{4} [/tex]
SOAL C.
[tex] \frac{ {(0.3)}^{7}}{ {(0.3)}^{3} } = {(0.3)}^{7 - 3} = {(0.3)}^{4} [/tex]
SOAL D.
[tex] \frac{ {( \frac{2}{5}) }^{9} }{ {( \frac{2}{5})}^{5} } = {( \frac{2}{5})}^{9 - 5} = {( \frac{2}{5})}^{4} [/tex]
SOAL E.
[tex] \frac{ {3}^{7} \times{3}^{2} }{ {3}^{3} } = {3}^{7 + 2 - 3} = {3}^{6} [/tex]
SOAL F.
[tex] \frac{ {5}^{5} }{ {5}^{2} \times {5}^{3} } = {5}^{5 - (2 + 3)} = {5}^{5 - 5} = {5}^{0} = 1[/tex]
SOAL G.
[tex] \frac{ {2}^{7} \times {6}^{7} }{ {4}^{7} } = \frac{ {2}^{7} \times {(2 \times 3)}^{7} }{ {( {2}^{2}) }^{7} } [/tex]
[tex] = \frac{ {2}^{7} \times {2}^{7} \times {3}^{7} }{ {2}^{2 \times 7} } [/tex]
[tex] = \frac{ {2}^{7 + 7} \times {3}^{7} }{ {2}^{14} }[/tex]
[tex]= \frac{ {2}^{14} \times {3}^{7} }{ {2}^{14} } [/tex]
[tex]= {2}^{14 - 14} \times {3}^{7} = {2}^{0} \times {3}^{7} = 1 \times {3}^{7} = {3}^{7} [/tex]
SOAL H.
[tex] \frac{ {6}^{7} \times {3}^{3}}{ {2}^{7} } = \frac{ ({2 \times 3})^{7} \times {3}^{3}}{ {2}^{7} } [/tex]
[tex] = \frac{ {2}^{7} \times {3}^{7} \times {3}^{3} }{ {2}^{7} } [/tex]
[tex] = {2}^{7 - 7} \times {3}^{7 + 3} = {2}^{0} \times {3}^{10} = 1 \times {3}^{10} = {3}^{10} [/tex]
SOAL I.
[tex] \frac{ {10}^{6} \times {4}^{2} }{ {25}^{3} \times {8}^{3} } = \frac{({2 \times 5})^{6} \times {({2}^{2}) }^{2} }{ ({ {5}^{2})}^{3} \times {({2}^{3})}^{3} } [/tex]
[tex] = \frac{ {2}^{6} \times {5}^{6} \times {2}^{2 \times 2} }{ {5}^{2 \times 3} \times {2}^{3 \times 3} } [/tex]
[tex] = \frac{ {2}^{6} \times {5}^{6} \times {2}^{4}}{ {5}^{6} \times {2}^{9} } [/tex]
[tex] = {2}^{6 + 4 - 9} \times {5}^{6 - 6} = {2}^{1} \times {5}^{0} = 2 \times 1 = 2 [/tex]
SOAL J.
[tex] \frac{ {21}^{5} }{ {9}^{2} } \div {( \frac{7}{2}) }^{2} = \frac{ ({3 \times 7})^{5} }{ { ({3}^{2}) }^{2} } \div \frac{ {7}^{2} }{ {2}^{2} } [/tex]
[tex] = \frac{ {3}^{5} \times {7}^{5} }{ {3}^{2 \times 2} } \div \frac{ {7}^{2} }{ {2}^{2} } [/tex]
[tex] = \frac{ {3}^{5} \times {7}^{5} }{ {3}^{4} } \div \frac{ {7}^{2} }{ {2}^{2} } [/tex]
[tex] = \frac{ {3}^{5} \times {7}^{5} }{ {3}^{4} } \times \frac{ {2}^{2} }{ {7}^{2} } [/tex]
[tex] = \frac{ {3}^{5} \times {7}^{5} \times {2}^{2}}{ {3}^{4} \times {7}^{2} } [/tex]
[tex] = {2}^{2} \times {3}^{5 - 4} \times {7}^{5 - 2} [/tex]
[tex] = {2}^{2} \times {3}^{1} \times {7}^{3} = {2}^{2} \times 3 \times {7}^{3} [/tex]
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