Question

Find the value of ${(-0.75)}^3+{\left(0.3\right)}^{-3}-{(-\frac{3}{2})}^{-3}$

Answer 1

Consider, ${(-0.75)}^3+{\left(0.3\right)}^{-3}-{(-\frac{3}{2})}^{-3}$

$=(-2.5\times 0.3{)}^3+\frac{1}{(0.3{)}^3}-{\left(\frac{3}{-2}\right)}^{-3}$ ...... [Using negative quotient rule of exponents]

$=\frac{(-0.75{)}^3\times (0.3{)}^3+1}{(0.3{)}^3}-\frac{(3{)}^{-3}}{(-2{)}^{-3}}$ ......... [Using quotient rule of exponents]

$=\frac{(-0.75\times 0.3{)}^3+1}{(0.3{)}^3}-\frac{(-2{)}^3}{(3{)}^3}$

$=\frac{(-0.225{)}^3+1}{(0.3{)}^3}-\frac{(-2{)}^3}{(0.3\times 10{)}^3}$

$=\frac{\left(\right(-0.225{)}^3+1)\times {10}^3}{(0.3{)}^3\times {10}^3}-\frac{(-2{)}^3}{(0.3{)}^3\times (10{)}^3}$

$=\frac{1.01139\times {10}^3+8}{(0.3{)}^3\times {10}^3}$

$=\frac{1011.39+8}{(0.3\times 10{)}^3}$ ..... [Using product rule of exponents]

$=\frac{1019.39}{3^3}=\frac{1019}{27}$