Pertanyaan

Sederhanakan bentuk dari ( 25 16 ) 64 125 l o g 3 !

Sederhanakan bentuk dari $(\frac{16}{25})^{^{\frac{125}{64}} l o g 3}$ !

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N. Puspita

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Jawaban terverifikasi

Pembahasan

jadi, bentuk sederhananya adalah

$begin mathsize 14px style left parenthesis 16 over 25 right parenthesis to the power of log presuperscript 125 over 64 end presuperscript space 3 equals open parentheses 4 over 5 close parentheses to the power of 2 space log presuperscript open parentheses 5 over 4 close parentheses cubed end presuperscript space 3 end exponent end exponent space space space space space space space space space space space space space space space space space equals open parentheses 5 over 4 close parentheses to the power of negative 2 times 1 third log presuperscript 5 over 4 end presuperscript 3 end exponent space space space space space space space space space space space space space space space space space equals 5 over 4 to the power of log presuperscript 5 over 4 end presuperscript 3 to the power of fraction numerator negative 2 over denominator 3 end fraction end exponent end exponent space space space space space space space space space space space space space space space space equals 3 to the power of negative 2 over 3 end exponent space space space space space space space space space space space space space space space space equals 1 over 3 to the power of begin display style 2 over 3 end style end exponent space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator cube root of 3 squared end root end fraction end style$

$equals fraction numerator 1 over denominator cube root of 9 end fraction$

jadi, bentuk sederhananya adalah $fraction numerator 1 over denominator cube root of 9 end fraction$