Pertanyaan

Jika m =0,83333..., n = 0,66666..., dan a = 256 , maka nilai dari adalah ....

Jika m = 0,83333..., n = 0,66666..., dan a = 256, maka nilai dari

adalah ....

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begin mathsize 14px style 10 n equals 6 comma 66666 horizontal ellipsis bottom enclose space space space space n equals 0 comma 66666... negative end enclose space space 9 n equals 6 space space space space n equals 6 over 9 space space space space n equals box enclose 2 over 3 end enclose end style

Sehingga

$begin mathsize 14px style open parentheses a to the power of m over a to the power of n close parentheses to the power of m plus n end exponent cross times open parentheses a to the power of n over a to the power of negative 2 end exponent close parentheses to the power of n minus 2 end exponent cross times open parentheses a to the power of negative 2 end exponent over a to the power of n close parentheses to the power of n minus 2 end exponent equals open parentheses a to the power of m over a to the power of n close parentheses to the power of m plus n end exponent cross times open parentheses fraction numerator up diagonal strike a to the power of n end strike over denominator up diagonal strike a to the power of negative 2 end exponent end strike end fraction cross times fraction numerator up diagonal strike a to the power of negative 2 end exponent end strike over denominator up diagonal strike a to the power of n end strike end fraction close parentheses to the power of n minus 2 end exponent equals open parentheses a to the power of m minus n end exponent close parentheses to the power of m plus n end exponent cross times open parentheses 1 close parentheses to the power of n minus 2 end exponent equals a to the power of m squared plus m n minus m n minus n squared end exponent equals a to the power of m squared minus n squared end exponent equals a to the power of open parentheses 5 over 6 close parentheses squared minus open parentheses 2 over 3 close parentheses squared end exponent equals a to the power of 25 over 36 minus 4 over 9 end exponent equals a to the power of fraction numerator 25 minus 16 over denominator 36 end fraction end exponent equals a to the power of 9 over 36 end exponent equals a to the power of 1 fourth end exponent equals open parentheses 256 close parentheses to the power of 1 fourth end exponent equals open parentheses 4 to the power of 4 close parentheses to the power of 1 fourth end exponent equals box enclose 4 end style$