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Mathematics : Exponents and Powers

Short Answer Type

31.

Find 'm' so that $left parenthesis negative 3 right parenthesis to the power of straight m plus 1 end exponent space cross times space left parenthesis negative 3 right parenthesis to the power of 5 space equals space left parenthesis negative 3 right parenthesis to the power of 7.$

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32.

Find the value of $open parentheses 2 over 3 close parentheses to the power of negative 2 end exponent$

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33.

Simplify:

(i) $open parentheses 5 over 8 close parentheses to the power of negative 7 end exponent space cross times space open parentheses 8 over 5 close parentheses to the power of negative 5 end exponent$ (ii) $open curly brackets open parentheses 1 third close parentheses to the power of negative 2 end exponent minus open parentheses 1 half close parentheses minus 3 over 4 close curly brackets divided by open parentheses 1 fourth close parentheses to the power of negative 2 end exponent$