Question

Find the value of the following expression: $(-0.75) ^3 + (0.3)^{-3} - \bigg( - \frac{3}{2}\bigg) ^{-3}$

Answer 1

Solution :

( - 0.75 )³ + ( 0.3 )^-3 - ( - 3/2 )^-3

= ( -75/100 )³ + ( 3/10 )^-3 - ( -3/2 )^-3

= ( -3/4 )³ + ( 10/3 )³ - ( -2/3 )³

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We know the Exponential laws:

1 ) a^-n = 1/aⁿ

2 ) ( a/b )^-n = ( b/a )ⁿ

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= - 27/64 + 1000/27 + 8/27

= -27/64 + 1008/27

= ( - 729 + 64512 )/1728

= 63783/1728

Or

≈ 36.91

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