Pertanyaan

Sederhanakan dalam bentuk pangkat positif. a. ( 6 xy 2 4 x − 2 y 3 ) − 3 ( 9 x − 1 y 2 8 x 2 y ) 2

Sederhanakan dalam bentuk pangkat positif.

a. $(\frac{4 x ^{- 2} y ^{3}}{6 xy ^{2}})^{- 3} (\frac{8 x ^{2} y}{9 x ^{- 1} y ^{2}})^{2}$

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Jawaban terverifikasi

Jawaban

bentuk pangkat positif dari

bentuk pangkat positif dari $open parentheses fraction numerator 4 x to the power of negative 2 end exponent y cubed over denominator 6 x y squared end fraction close parentheses to the power of negative 3 end exponent open parentheses fraction numerator 8 x squared y over denominator 9 x to the power of negative 1 end exponent y squared end fraction close parentheses squared equals fraction numerator 8 x to the power of 15 over denominator 3 y to the power of 5 end fraction$

Pembahasan

Sifat-sifat bilangan berpangkat di antaranya sebagai berikut. , , , Penyelesaian soal di atas adalah sebagai berikut. Dengan demikian, bentuk pangkat positif dari

Sifat-sifat bilangan berpangkat di antaranya sebagai berikut.

a to the power of m times a to the power of n equals a to the power of m plus n end exponent

a to the power of m over a to the power of n equals a to the power of m minus n end exponent , a not equal to 0

a to the power of negative m end exponent equals 1 over a to the power of m , a not equal to 0

open parentheses a times b close parentheses to the power of m equals a to the power of m times b to the power of m

open parentheses a over b close parentheses to the power of m equals a to the power of m over b to the power of m , b not equal to 0

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent

Penyelesaian soal di atas adalah sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 4 x to the power of negative 2 end exponent y cubed over denominator 6 x y squared end fraction close parentheses to the power of negative 3 end exponent open parentheses fraction numerator 8 x squared y over denominator 9 x to the power of negative 1 end exponent y squared end fraction close parentheses squared end cell row blank equals cell open parentheses 4 x to the power of negative 2 end exponent y cubed close parentheses to the power of negative 3 end exponent over open parentheses 6 x y squared close parentheses to the power of negative 3 end exponent times open parentheses 8 x squared y close parentheses squared over open parentheses 9 x to the power of negative 1 end exponent y squared close parentheses squared end cell row blank equals cell fraction numerator 4 to the power of negative 3 end exponent times x to the power of 6 times y to the power of negative 9 end exponent over denominator 6 to the power of negative 3 end exponent times x to the power of negative 3 end exponent times y to the power of negative 6 end exponent end fraction times fraction numerator 8 squared times x to the power of 4 times y squared over denominator 9 squared times x to the power of negative 2 end exponent times y to the power of 4 end fraction end cell row blank equals cell fraction numerator open parentheses 2 squared close parentheses to the power of negative 3 end exponent times x to the power of 6 times y to the power of negative 9 end exponent times open parentheses 2 cubed close parentheses squared times x to the power of 4 times y squared over denominator open parentheses 2 times 3 close parentheses to the power of negative 3 end exponent times x to the power of negative 3 end exponent times y to the power of negative 6 end exponent times open parentheses 3 squared close parentheses squared times x to the power of negative 2 end exponent times y to the power of 4 end fraction end cell row blank equals cell fraction numerator 2 to the power of negative 6 end exponent times 2 to the power of 6 times x to the power of 6 plus 4 end exponent times y to the power of negative 9 plus 2 end exponent over denominator 2 to the power of negative 3 end exponent times 3 to the power of negative 3 end exponent times 3 to the power of 4 times x to the power of negative 3 plus open parentheses negative 2 close parentheses end exponent times y to the power of negative 6 plus 4 end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 0 times x to the power of 10 times y to the power of negative 7 end exponent over denominator 2 to the power of negative 3 end exponent times 3 to the power of negative 3 plus 4 end exponent times x to the power of negative 5 end exponent times y to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 0 over denominator 2 to the power of negative 3 end exponent times 3 end fraction times x to the power of 10 over x to the power of negative 5 end exponent times y to the power of negative 7 end exponent over y to the power of negative 2 end exponent end cell row blank equals cell 2 to the power of 0 minus open parentheses negative 3 close parentheses end exponent times 1 third times x to the power of 10 minus open parentheses negative 5 close parentheses end exponent times y to the power of negative 7 minus open parentheses negative 2 close parentheses end exponent end cell row blank equals cell 2 cubed times 1 third times x to the power of 15 times y to the power of negative 5 end exponent end cell row blank equals cell fraction numerator 8 x to the power of 15 over denominator 3 y to the power of 5 end fraction end cell end table$

Dengan demikian, bentuk pangkat positif dari $open parentheses fraction numerator 4 x to the power of negative 2 end exponent y cubed over denominator 6 x y squared end fraction close parentheses to the power of negative 3 end exponent open parentheses fraction numerator 8 x squared y over denominator 9 x to the power of negative 1 end exponent y squared end fraction close parentheses squared equals fraction numerator 8 x to the power of 15 over denominator 3 y to the power of 5 end fraction$