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61.
Simplify: $open square brackets fraction numerator 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 over denominator 2 to the power of negative 2 end exponent cross times 2 squared cross times 2 to the power of negative 5 end exponent end fraction close square brackets$

Since, $straight m to the power of straight a cross times straight m to the power of straight b equals straight m to the power of straight a plus straight b end exponent$

     $space space space space space space therefore space space space space space space space space 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 space equals space 3 to the power of 3 plus left parenthesis negative 2 right parenthesis plus 5 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 to the power of 8 minus 2 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 to the power of 6$

                    $space space space space space space space space 2 to the power of negative 2 end exponent space cross times space 2 squared space cross times space 2 to the power of negative 5 end exponent space equals space 2 to the power of negative 2 plus 2 minus 5 end exponent$

                                                   = $space space 2 to the power of negative 5 end exponent$

$rightwards double arrow$           $fraction numerator 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 over denominator 2 to the power of negative 2 end exponent cross times 2 squared cross times 2 to the power of negative 5 end exponent end fraction space equals space 3 to the power of 6 over 2 to the power of negative 5 end exponent$

                                      $equals space 3 to the power of 6 space cross times space 2 to the power of 5$

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62.

Evaluate:
$left parenthesis negative 6 right parenthesis squared space cross times space open parentheses 2 over 3 close parentheses squared cross times open parentheses 2 over 5 close parentheses squared$

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63.

Find the value of: $left parenthesis 8 to the power of negative 0 end exponent plus 5 to the power of negative 1 end exponent right parenthesis to the power of negative 2 end exponent straight x 3 squared$

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64.

Find the value of $open parentheses 1 fourth close parentheses to the power of negative 2 end exponent plus open parentheses 1 third close parentheses to the power of negative 3 end exponent plus open parentheses 1 half close parentheses to the power of negative 4 end exponent$

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65.

Simplify: $open square brackets open parentheses fraction numerator negative 4 over denominator 5 end fraction close parentheses to the power of negative 2 end exponent close square brackets squared$

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66.

Find the value of m when $fraction numerator 5 to the power of straight m plus 5 to the power of negative 3 end exponent over denominator 5 squared end fraction space equals space 5 cubed$

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Long Answer Type

67.

Simplify : $space space fraction numerator 2 to the power of negative 5 end exponent cross times 10 to the power of negative 5 end exponent cross times 125 over denominator 5 to the power of negative 9 end exponent cross times 6 to the power of negative 5 end exponent end fraction$

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Short Answer Type

68.

Write the following in standard form: (i) 0.000000456 and (ii) 34500000.

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69.

Express 2.0001 x 10^–9 in usual form.

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70.

Simplify:

$left parenthesis negative 5 right parenthesis to the power of 5 space cross times space left parenthesis negative 5 right parenthesis to the power of 4$

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61. Simplify:

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