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

Since $straight a to the power of straight m space cross times space straight b to the power of straight m space equals left parenthesis ab right parenthesis to the power of straight m$

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$equals open square brackets left parenthesis negative 6 right parenthesis space cross times space 2 over 3 cross times 2 over 5 close square brackets squared$

$equals open square brackets fraction numerator negative 2 space cross times space 2 space cross times 2 over denominator 5 end fraction close square brackets squared$

$space equals open square brackets fraction numerator negative 8 over denominator 5 end fraction close square brackets squared space equals space 64 over 25$

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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:

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