Solve {left(frac{1/3right)}^2-{left(1/2right)}^-3}{{left(1/4right)}^-2}

$$\frac{ { \left( \frac{ 1 }{ 3 } \right) }^{ 2 } - { \left( \frac{ 1 }{ 2 } \right) }^{ -3 } }{ { \left( \frac{ 1 }{ 4 } \right) }^{ -2 } }$$

Evaluate

$$-\frac{71}{144}\approx -0.493055556$$

Solution Steps

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}-\left(\frac{1}{2}\right)^{-3}}{\left(\frac{1}{4}\right)^{-2}}$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$\frac{\frac{1}{9}-8}{\left(\frac{1}{4}\right)^{-2}}$$

Subtract 8 from \frac{1}{9} to get -\frac{71}{9}.

$$\frac{-\frac{71}{9}}{\left(\frac{1}{4}\right)^{-2}}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{-\frac{71}{9}}{16}$$

Express \frac{-\frac{71}{9}}{16} as a single fraction.

$$\frac{-71}{9\times 16}$$

Multiply 9 and 16 to get 144.

$$\frac{-71}{144}$$

Fraction \frac{-71}{144} can be rewritten as -\frac{71}{144} by extracting the negative sign.

$$-\frac{71}{144}$$

Factor

$$-\frac{71}{144} = -0.4930555555555556$$