Tentukan hasil berikut : c.

Pertanyaan

Tentukan hasil berikut :

c. $open parentheses negative 8 plus 12 close parentheses to the power of 4$

Pembahasan Soal:

Ingat!

Definisi bilangan berpangkat:

$a to the power of n equals a cross times a cross times a cross times... cross times a$

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 8 plus 12 close parentheses to the power of 4 end cell equals cell open parentheses 4 close parentheses to the power of 4 end cell row blank equals cell 4 cross times 4 cross times 4 cross times 4 end cell row blank equals 256 end table$

Dengan demikian, hasil dari $open parentheses negative 8 plus 12 close parentheses to the power of 4$ adalah $256$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 14 Agustus 2021

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Sederhanakanlah bentuk-bentuk berikut, kemudian tentukanlah nilainya:

Pembahasan Soal:

Ingat kembali definisi bilangan berpangkat:

$a^{n} a^{m} \times a^{n} = = sebanyak n a \times a \times a \times a \times \dots \times a a^{m + n}$

maka

$7^{3} \cdot 7^{5} \cdot 7^{- 2} = = = = = = = 7^{3 + 5 + (- 2)} 7^{3 + 5 - 2} 7^{8 - 2} 7^{6} 7 \times 7 \times 7 \times 7 \times 7 \times 7 117.649$

Dengan demikian hasil $7 cubed times 7 to the power of 5 times 7 to the power of negative 2 end exponent$ adalah 117.649.

Roboguru

Tentukan hasil berikut : a.

Pembahasan Soal:

Ingat!

Definisi bilangan berpangkat:

$a to the power of n equals a cross times a cross times a cross times... cross times a$

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell negative 17 squared end cell equals cell negative open parentheses 17 cross times 17 close parentheses end cell row blank equals cell negative 289 end cell end table$

Dengan demikian, hasil dari $negative 17 squared$ adalah $negative 289$ .

Roboguru

Tentukan hasil berikut : b.

Pembahasan Soal:

Ingat!

Definisi bilangan berpangkat:

$a to the power of n equals a cross times a cross times a cross times... cross times a$

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open parentheses negative 11 close parentheses cubed end cell equals cell 2 cross times open square brackets open parentheses negative 11 close parentheses cross times left parenthesis negative 11 right parenthesis cross times negative left parenthesis 11 right parenthesis close square brackets end cell row blank equals cell 2 cross times left parenthesis negative 1.331 right parenthesis end cell row blank equals cell negative 2.662 end cell end table$

Dengan demikian, hasil dari $2 open parentheses negative 11 close parentheses cubed$ adalah $negative 2.662$ .

Roboguru

Apabila dan , maka ....

Pembahasan Soal:

Ingat kembali:

$square root of a equals a to the power of 1 half end exponent$
$a equals a to the power of 1$
$open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent$
$table row cell a to the power of m end cell equals cell stack a cross times a cross times midline horizontal ellipsis cross times a with underbrace below end cell row blank blank cell blank presuperscript text sebanyak end text space m end presuperscript end cell end table$

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell square root of square root of square root of A end root end root end cell equals 2 row cell square root of square root of A to the power of 1 half end exponent end root end root end cell equals cell 2 to the power of 1 end cell row cell square root of open parentheses A to the power of 1 half end exponent close parentheses to the power of 1 half end exponent end root end cell equals cell 2 to the power of 1 end cell row cell open parentheses open parentheses A to the power of 1 half end exponent close parentheses to the power of 1 half end exponent close parentheses to the power of 1 half end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 half cross times 1 half cross times 1 half end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 over 8 end exponent end cell equals cell 2 to the power of 1 end cell row cell A to the power of 1 over 8 cross times 8 end exponent end cell equals cell 2 to the power of 1 cross times 8 end exponent end cell row cell A to the power of 1 end cell equals cell 2 to the power of 8 end cell row A equals cell 2 to the power of 8 end cell row A equals cell 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 4 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 8 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 16 cross times 2 cross times 2 cross times 2 cross times 2 end cell row A equals cell 32 cross times 2 cross times 2 cross times 2 end cell row A equals cell 64 cross times 2 cross times 2 end cell row A equals cell 128 cross times 2 end cell row A equals 256 end table$

Oleh karena $A equals 256$ dan $B equals 257$ , diperoleh hubungan

$table attributes columnalign right center left columnspacing 0px end attributes row A equals 256 row blank equals cell 257 minus 1 end cell row blank equals cell B minus 1 end cell end table$

dan

$table attributes columnalign right center left columnspacing 0px end attributes row B equals 257 row blank equals cell 256 plus 1 end cell row blank equals cell A plus 1 end cell end table$

Jadi, apabila $square root of square root of square root of A end root end root equals 2$ dan $B equals 257$ , maka $B equals A plus 1$ dan $A equals B minus 1$ .

Oleh karena itu, jawaban yang benar adalah D dan E. $space$

Roboguru

= .....

Pembahasan Soal:

Perhatikan bahwa $begin mathsize 14px style m to the power of n end style$ berarti perkalian berulang bilangan m sebanyak n kali. Sehingga

$begin mathsize 14px style m to the power of n equals blank stack stack m cross times m cross times m cross times horizontal ellipsis cross times m with underbrace below with text sebanyak end text n text kali end text below end style$

Roboguru