Pertanyaan

Tentukan nilai n dari ( 2 1 ) 2 × ( 4 ) 2 ( 4 2 ) 5 × ( 2 1 ) 3 = 2 n !

Tentukan nilai $n$ dari $\frac{( 4 ^{2} ) ^{5} \times ( \frac{1}{2} ) ^{3}}{( \frac{1}{2} ) ^{2} \times ( 4 ) ^{2}} = 2^{n}$ !

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Jawaban terverifikasi

Jawaban

nilai adalah .

nilai

adalah

Pembahasan

Persamaan bilangan berpangkat di atas dapat disederhanakan seperti berikut, Karena bilangan pokoknya sama, maka dapat dibuat persamaan pangkatnya yaitu . Jadi,nilai adalah .

Persamaan bilangan berpangkat di atas dapat disederhanakan seperti berikut,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 4 squared close parentheses to the power of 5 cross times open parentheses begin display style 1 half end style close parentheses cubed over denominator open parentheses begin display style 1 half end style close parentheses squared cross times open parentheses 4 squared close parentheses end fraction end cell equals cell 2 to the power of n end cell row cell fraction numerator open parentheses left parenthesis 2 squared right parenthesis squared close parentheses to the power of 5 cross times open parentheses 2 to the power of negative 1 end exponent close parentheses cubed over denominator open parentheses 2 to the power of negative 1 end exponent close parentheses squared cross times left parenthesis 2 squared right parenthesis squared end fraction end cell equals cell 2 to the power of n end cell row cell fraction numerator open parentheses 2 to the power of 4 close parentheses to the power of 5 cross times open parentheses 2 to the power of negative 3 end exponent close parentheses over denominator open parentheses 2 to the power of negative 2 end exponent close parentheses cross times open parentheses 2 to the power of 4 close parentheses end fraction end cell equals cell 2 to the power of n end cell row cell fraction numerator open parentheses 2 to the power of 20 close parentheses cross times open parentheses 2 to the power of negative 3 end exponent close parentheses over denominator open parentheses 2 to the power of negative 2 plus 4 end exponent close parentheses end fraction end cell equals cell 2 to the power of n end cell row cell fraction numerator open parentheses 2 to the power of 20 minus 3 end exponent close parentheses over denominator open parentheses 2 squared close parentheses end fraction end cell equals cell 2 to the power of n end cell row cell 2 to the power of 17 minus 2 end exponent end cell equals cell 2 to the power of n end cell row cell 2 to the power of 15 end cell equals cell 2 to the power of n end cell row blank blank blank end table$

Karena bilangan pokoknya sama, maka dapat dibuat persamaan pangkatnya yaitu n equals 15 .

Jadi, nilai adalah .