1.Sederhanakan operasi aljabar berikut ini :

By Admin ReiPosted on October 28, 2022

a. 2m x 4m pangkat 3
b. p x 2q pangkat 2 x p pangkat 3 x 3q pangkat 4
c. ( 5k pangkat 2) pangkat 3 x 2k pangkat 2
d. (2x pangkat 3) x 3(x pangkat 2y pangkat 2) pangkat 3 x 2y pangkat 4

2.Tentukan nilai a yang memenuhi persamaan :
a. 2 pangkat 2 x 2a = 2 pangkat 5
b. ( 4a ) pangkat 2 = 4 pangkat 6
c. ( 3a )a = 81
d.1/27 x 3a = 9

1.Sederhanakan operasi aljabar berikut ini :

Jawaban:

Soal ( 1 )

a.

$sf{2m times {4m}^{3} }$

$= sf{8m times {m}^{3} }$

$= sf{8 {m}^{1} times {m}^{3} }$

$= sf{8 {m}^{1 + 3} }$

$= boxed{ green{ sf{8 {m}^{4} }}}$

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b.

$sf{p times 2 {q}^{2} times {p}^{3} times 3 {q}^{4} }$

$= sf{ {p}^{1} times 6 {q}^{2 + 4} times {p}^{3} }$

$= sf{ {p}^{1 + 3} times 6 {q}^{6} }$

$= sf{ {p}^{4} times {6q}^{6} }$

$= boxed{ green{ sf{6 {p}^{4} {q}^{6} }}}$

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c.

$sf{ {(5k^{2} )}^{3} times {2k}^{2} }$

$= sf{ {5}^{3} times ({k}^{2})^{3} times {2k}^{2} }$

$= sf{125 times {k}^{2 times 3} times {2k}^{2} }$

$= sf{125 {k}^{6} times {2k}^{2} }$

$= sf{250 {k}^{6} times {k }^{2} }$

$= sf{250 {k}^{6 + 2} }$

$= boxed{ green{ sf{250 {k}^{8} }}}$

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d.

$sf{ {(2x)}^{3} times 3 {( {x}^{2} {y}^{2} )}^{3} times {2y}^{4} }$

$= sf{ {2x}^{3} times 3( {x}^{2 times 3} {y}^{2 times 3} ) times {2y}^{4} }$

$= sf{ {2x}^{3} times 3 {x}^{6} {y}^{6} times {2y}^{4} }$

$= sf{12 {x}^{3} times {x}^{6} {y}^{6} times {y}^{4} }$

$= sf{12 {x}^{3 + 6} {y}^{6 + 4} }$

$= boxed{ green{sf{12 {x}^{9} {y}^{10} }}}$

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Soal ( 2 )

a.

$sf{ {2}^{2} times 2a = {2}^{5} }$

$sf{ {2}^{2} times {2}^{1} a = {2}^{5} }$

$sf{ {2}^{2 + 1} times a = {2}^{5} }$

$sf{ {2}^{3} times a = {2}^{5} }$

$sf{8 times a = 32}$

$sf{a = dfrac{32}{8} }$

$boxed{ green{sf{a = 4}}}$

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b.

$sf{ {(4a)}^{2} = {4}^{6} }$

$sf{4a = ± sqrt{4^{6}}}$

$sf{4a = ± 64}$

$sf{4a = - 64} \ sf{4a = 64}$

$sf{a = dfrac{ - 64}{4} } \ \ sf{a = dfrac{64}{4} }$

$sf{a = - 16} \ sf{a = 16}$

$boxed{ green{ sf{a_{1} = - 16 : : dan : : a_{2} = 16 }}}$

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c.

$sf{{(3a)}a = 81 }$

$sf{ {(3a)}a div 3 = 81 div 3}$

$sf{a times a = 27}$

$sf{ {a}^{2} = 27}$

$sf{a = ± sqrt{27}}$

$sf{a = ± sqrt{3^{3}}}$

$sf{a = ± sqrt{3^{2 + 1}}}$

$sf{a = ± sqrt{3^{2} times 3^{1}}}$

$sf{a = ± sqrt{3^{2} times 3}}$

$sf{a = ± sqrt{3^{2}} sqrt{3}}$

$sf{a = ± 3 sqrt{3}}$

$sf{a = - 3 sqrt{3} } \ sf{a = 3 sqrt{3} }$

$boxed{ green{ sf{a_{1} = - 3 sqrt{3} : : dan : : a_{2} = 3 sqrt{3} }}}$

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d.

$sf{ dfrac{1}{27} times 3a = 9 }$

$sf{ dfrac{1}{9} times a = 9 }$

$sf{a = 9 div dfrac{1}{9} }$

$sf{a = 9 times dfrac{9}{1} }$

$sf{a = 9 times 9}$

$boxed{ green{ sf{a = 81}}}$

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