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

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

Since $125 space equals space 5 space cross times space 5 space cross times space 5 space equals space 5 cubed$

$10 to the power of negative 5 end exponent space equals space left parenthesis 2 cross times 5 right parenthesis to the power of negative 5 end exponent space equals space 2 to the power of negative 5 end exponent space cross times space 5 to the power of negative 5 end exponent 6 to the power of negative 5 end exponent space equals space left parenthesis 2 cross times 3 right parenthesis to the power of negative 5 end exponent space equals space 2 to the power of negative 5 end exponent space cross times space 3 to the power of negative 5 end exponent$

∴ $fraction numerator 2 to the power of negative 5 end exponent cross times 10 to the power of negative 5 end exponent cross times 125 over denominator 5 to the power of negative 9 end exponent space cross times space 6 to the power of negative 5 end exponent end fraction space equals space fraction numerator 2 to the power of negative 5 end exponent cross times 2 to the power of negative 5 end exponent cross times 5 to the power of negative 5 end exponent cross times 5 cubed over denominator 5 to the power of negative 9 end exponent cross times 2 to the power of negative 5 end exponent cross times 3 to the power of negative 5 end exponent end fraction$

 $equals open parentheses 2 to the power of negative 5 end exponent over 2 to the power of negative 5 end exponent close parentheses space cross times space fraction numerator 5 to the power of negative 5 plus left parenthesis negative 5 right parenthesis plus 3 end exponent over denominator 5 to the power of negative 9 end exponent cross times 2 to the power of negative 5 end exponent cross times 3 to the power of negative 5 end exponent end fraction$

 $equals 1 space cross times space fraction numerator 5 to the power of negative 7 end exponent over denominator 5 to the power of negative 9 space end exponent cross times space 3 to the power of negative 5 end exponent end fraction$

 $equals fraction numerator 1 cross times 5 to the power of 9 cross times 3 to the power of 5 over denominator 5 to the power of 7 end fraction$

 $equals 1 cross times 5 to the power of 9 minus 7 end exponent cross times 3 to the power of 5$

 = $1 space cross times space 5 squared space cross times space 3 to the power of 5$

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 = 25 $cross times$ 243 = 6075.

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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:

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