Question

$\frac{(0.22{)}^3+(0.11{)}^3+(0.32{)}^3}{(0.66{)}^3+(0.96{)}^3+(0.33{)}^3}-\frac{(0.32{)}^3+(0.45{)}^3-(0.77{)}^3}{81\left(0.32\right)\left(0.45\right)\left(0.77\right)}$ equals

• A. 1
• B. $\frac{1}{11}$
• C. 0
• D. -1

Answer 1

The correct option is C 0

$\frac{(0.22{)}^3+(0.11{)}^3+(0.32{)}^3}{(0.66{)}^3+(0.96{)}^3-(0.33{)}^3}+\frac{(0.32{)}^3+(0.45{)}^3-(0.77{)}^3}{81\left(0.32\right)\left(0.45\right)\left(0.77\right)}$
$=\frac{8(0.11{)}^3+(0.11{)}^3+(0.32{)}^3}{216(0.11{)}^3+27(0.32{)}^3+27(0.11{)}^3}-\frac{(0.32{)}^3+(0.45{)}^3-(0.32+0.45{)}^3}{81\left(0.32\right)\left(0.45\right)\left(0.77\right)}$
$=\frac{9(0.11{)}^3+(0.32{)}^3}{243(0.11{)}^3+27(0.32{)}^3}-\frac{(0.32{)}^3+(0.45{)}^3-(0.32+0.45{)}^3}{81\left(0.32\right)\left(0.45\right)\left(0.77\right)}$
$=\frac{9(0.11{)}^3+(0.32{)}^3}{27\left\{9\right(0.11{)}^3+\left(0.32{)}^3\right\}}-\frac{(0.32{)}^3+(0.45{)}^3-\left[\right(0.32{)}^3+(0.45{)}^3+3(0.32\left)\right(0.45\left)\right(0.32)+(0.45)}{81\left(0.32\right)\left(0.45\right)\left(0.77\right)}$
$=\frac{1}{27}-\frac{1}{27}$
$=0$