Question

Simplify and express the result in power notation with positive exponent.

$open parentheses 1 over 2 cubed close parentheses squared$

Solution

$open parentheses 1 over 2 cubed close parentheses squared$

∵ $1 space equals space 1 cubed$

∴   $1 over 2 cubed equals 1 cubed over 2 cubed equals open parentheses 1 half close parentheses cubed$
Now   $open parentheses 1 over 2 cubed close parentheses squared equals open square brackets open parentheses 1 half close parentheses cubed close square brackets squared equals open parentheses 1 half close parentheses to the power of 3 cross times 2 end exponent$            [Using $left parenthesis straight a to the power of straight m right parenthesis to the power of straight n equals straight a to the power of mn$ ]
                   = $open parentheses 1 half close parentheses to the power of 6 equals 1 over 2 to the power of 6$

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Exponents And Powers

Simplify and express the result in power notation with positive exponent.

$open parentheses 1 over 2 cubed close parentheses squared$

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