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Exponents And Powers

Question
CBSEENMA8002647
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Evaluate:

open curly brackets open square brackets 1 third close square brackets to the power of negative 1 end exponent minus open parentheses 1 fourth close parentheses to the power of negative 1 end exponent close curly brackets to the power of negative 1 end exponent

Solution

open curly brackets open parentheses 1 third close parentheses to the power of negative 1 end exponent minus open parentheses 1 fourth close parentheses to the power of negative 1 end exponent close curly brackets to the power of negative 1 end exponent

∵                     left parenthesis straight a right parenthesis to the power of negative 1 end exponent space equals space 1 over straight a

∴         open curly brackets open parentheses 1 third close parentheses to the power of negative 1 end exponent minus open parentheses 1 fourth close parentheses to the power of negative 1 end exponent close curly brackets to the power of negative 1 end exponent space equals space open curly brackets fraction numerator 1 over denominator begin display style 1 third end style end fraction minus fraction numerator 1 over denominator begin display style 1 fourth end style end fraction close curly brackets to the power of negative 1 end exponent
                                        equals 3 space minus space 4 to the power of negative 1 end exponent space equals space minus space 1 to the power of negative 1 end exponent
                                         space equals space fraction numerator 1 over denominator negative 1 end fraction space equals space minus 1

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