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Exponents And Powers

Question
CBSEENMA8002641
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Find the value of:
space space open curly brackets open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of negative 2 end exponent close curly brackets squared










Solution

space space open curly brackets open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of negative 2 end exponent close curly brackets squared 

∵  left parenthesis straight a to the power of straight m right parenthesis to the power of straight n space equals space straight a to the power of mn

∴   space space open curly brackets open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of negative 2 end exponent close curly brackets squared space equals space open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of left parenthesis negative 2 right parenthesis space cross times space 2 end exponent space equals space open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of negative 4 end exponent space equals space fraction numerator left parenthesis negative 2 right parenthesis to the power of negative 4 end exponent over denominator left parenthesis 3 right parenthesis to the power of negative 4 end exponent end fraction space space
                                                   open square brackets therefore space space open parentheses straight a over straight b close parentheses to the power of straight m space equals space straight a to the power of straight m over straight b to the power of straight m close square brackets
                       equals fraction numerator 3 to the power of 4 over denominator left parenthesis negative 2 right parenthesis to the power of 4 end fraction space equals space fraction numerator 3 space cross times space 3 space cross times space 3 space cross times space 3 over denominator left parenthesis negative 2 right parenthesis space cross times space left parenthesis negative 2 right parenthesis space cross times space left parenthesis negative 2 right parenthesis space cross times space left parenthesis negative 2 right parenthesis end fraction
                        equals 81 over 16

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