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Nyatakan akar bilangan berikut dalarn bentuk bilangan berpangkat ! a. 3 25 ​ b. 16 a 3 ​ c. 3 15 a 4 ​ d. 3 − 27 a 8 ​

Nyatakan akar bilangan berikut dalarn bentuk bilangan berpangkat !

a.
b.
c.
d.

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D. Nuryani

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Mahasiswa/Alumni Universitas Padjadjaran

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, , dan .

cube root of 25 equals 5 to the power of 2 over 3 end exponent, Error converting from MathML to accessible text.Error converting from MathML to accessible text. dan Error converting from MathML to accessible text..

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Pembahasan

Ingatlah, untuk sembarang bilangan dengan , berlaku: dengan . Ingat juga, sifat-sifat bilangan berpangkat berikut. Berdasarkan hal-hal di atas, maka: a) b) c) d) Dengan demikian, , , dan .

Ingatlah, untuk sembarang bilangan a dengan a not equal to 0, berlaku:

n-th root of a to the power of m end root equals a to the power of m over n end exponent

dengan n not equal to 0.

Ingat juga, sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m left parenthesis ii right parenthesis space 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

Berdasarkan hal-hal di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 25 end cell equals cell 25 to the power of 1 third end exponent end cell row blank equals cell open parentheses 5 squared close parentheses to the power of 1 third end exponent end cell row blank equals cell 5 to the power of 2 cross times 1 third end exponent end cell row blank equals cell 5 to the power of 2 over 3 end exponent end cell end table

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 16 a cubed end root end cell equals cell open parentheses 16 a cubed close parentheses to the power of 1 half end exponent end cell row blank equals cell open parentheses 2 to the power of 4 close parentheses to the power of 1 half end exponent times open parentheses a cubed close parentheses to the power of 1 half end exponent end cell row blank equals cell 2 to the power of 4 cross times 1 half end exponent times a to the power of 3 cross times 1 half end exponent end cell row blank equals cell 2 squared times a to the power of 3 over 2 end exponent end cell row blank equals cell 4 a to the power of 3 over 2 end exponent end cell end table

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 15 a to the power of 4 end root end cell equals cell open parentheses 15 a to the power of 4 close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses 15 close parentheses to the power of 1 third end exponent times open parentheses a to the power of 4 close parentheses to the power of 1 third end exponent end cell row blank equals cell 15 to the power of 1 third end exponent a to the power of 4 cross times 1 third end exponent end cell row blank equals cell 15 to the power of 1 third end exponent a to the power of 4 over 3 end exponent end cell end table

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of negative 27 a to the power of 8 end root end cell equals cell open parentheses negative 27 a to the power of 8 close parentheses to the power of 1 third end exponent end cell row blank equals cell open parentheses negative 3 cubed close parentheses to the power of 1 third end exponent times open parentheses a to the power of 8 close parentheses to the power of 1 third end exponent end cell row blank equals cell negative 3 to the power of up diagonal strike 3 cross times fraction numerator 1 over denominator up diagonal strike 3 end fraction end exponent times a to the power of 8 cross times 1 third end exponent end cell row blank equals cell negative 3 a to the power of 8 over 3 end exponent end cell end table
 

Dengan demikian, cube root of 25 equals 5 to the power of 2 over 3 end exponent, Error converting from MathML to accessible text.Error converting from MathML to accessible text. dan Error converting from MathML to accessible text..

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