Pertanyaan

Jika a = 1 , b = 2 , dan c = 3 , tentukan nilai dari operasi berikut. b. { ( b × c ) 2 × b } ÷ ( a × b ) 2

Jika $a = 1$ , $b = 2$ , dan $c = 3$ , tentukan nilai dari operasi berikut.

b. ${(b \times c)^{2} \times b} \div (a \times b)^{2}$

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

{ ( b × c ) 2 × b } ÷ ( a × b ) 2 = 18

{(b \times c)^{2} \times b} \div (a \times b)^{2} = 18

Pembahasan

Ingat kembali sifat operasi hitung bilangan berpangkat bulat positif. Untuk bilangan bulat dan q serta bilangan bulat positif m dan n berlaku ( p × q ) n p m × p n p m ÷ p n p n = = = = p n × q n p m + n p n p m = p m − n p × p × p × ... × p n ka l i Berdasarkan sifat di atas, didapat bahwa { ( b × c ) 2 × b } ÷ ( a × b ) 2 = = = = = = = ( b 2 × c 2 × b ) ÷ ( a 2 × b 2 ) { ( b 2 × b ) × c 2 } ÷ ( a 2 × b 2 ) ( b 2 + 1 × c 2 ) ÷ ( a 2 × b 2 ) ( b 3 × c 2 ) ÷ ( a 2 × b 2 ) a 2 × b 2 b 3 × c 2 a 2 b 3 − 2 × c 2 a 2 b × c 2 Diketahui a = 1 , b = 2 , dan c = 3 . Maka { ( b × c ) 2 × b } ÷ ( a × b ) 2 = = = = = a 2 b × c 2 1 2 2 × 3 2 ( 1 × 1 ) 2 × ( 3 × 3 ) 1 18 18 Dengan demikian, { ( b × c ) 2 × b } ÷ ( a × b ) 2 = 18

Ingat kembali sifat operasi hitung bilangan berpangkat bulat positif. Untuk bilangan bulat $p$ dan $q$ serta bilangan bulat positif $m$ dan $n$ berlaku

$(p \times q)^{n} p^{m} \times p^{n} p^{m} \div p^{n} p^{n} = = = = p^{n} \times q^{n} p^{m + n} \frac{p ^{m}}{p ^{n}} = p^{m - n} p \times p \times p \times ... \times p n ka l i$

Berdasarkan sifat di atas, didapat bahwa

${(b \times c)^{2} \times b} \div (a \times b)^{2} = = = = = = = (b^{2} \times c^{2} \times b) \div (a^{2} \times b^{2}) {(b^{2} \times b) \times c^{2}} \div (a^{2} \times b^{2}) (b^{2 + 1} \times c^{2}) \div (a^{2} \times b^{2}) (b^{3} \times c^{2}) \div (a^{2} \times b^{2}) \frac{b ^{3} \times c ^{2}}{a ^{2} \times b ^{2}} \frac{b ^{3 - 2} \times c ^{2}}{a ^{2}} \frac{b \times c ^{2}}{a ^{2}}$

Diketahui $a = 1$ , $b = 2$ , dan $c = 3$ . Maka

${(b \times c)^{2} \times b} \div (a \times b)^{2} = = = = = \frac{b \times c ^{2}}{a ^{2}} \frac{2 \times 3 ^{2}}{1 ^{2}} \frac{2 \times ( 3 \times 3 )}{( 1 \times 1 )} \frac{18}{1} 18$