Solve {left(1-frac{sqrt{121}}{3^2}right)}^-1-2^32/2^2-sqrt{25/16}

$${ \left(1- \frac{ \sqrt{ 121 } }{ { 3 }^{ 2 } } \right) }^{ -1 } - \frac{ { 2 }^{ 3 } 2 }{ { 2 }^{ 2 } } - \sqrt{ \frac{ 25 }{ 16 } }$$

Evaluate

$$-\frac{39}{4}=-9.75$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(1-\frac{\sqrt{121}}{3^{2}}\right)^{-1}-\frac{2^{4}}{2^{2}}-\sqrt{\frac{25}{16}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\left(1-\frac{\sqrt{121}}{3^{2}}\right)^{-1}-2^{2}-\sqrt{\frac{25}{16}}$$

Calculate the square root of 121 and get 11.

$$\left(1-\frac{11}{3^{2}}\right)^{-1}-2^{2}-\sqrt{\frac{25}{16}}$$

Calculate 3 to the power of 2 and get 9.

$$\left(1-\frac{11}{9}\right)^{-1}-2^{2}-\sqrt{\frac{25}{16}}$$

Subtract \frac{11}{9} from 1 to get -\frac{2}{9}.

$$\left(-\frac{2}{9}\right)^{-1}-2^{2}-\sqrt{\frac{25}{16}}$$

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

$$-\frac{9}{2}-2^{2}-\sqrt{\frac{25}{16}}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{9}{2}-4-\sqrt{\frac{25}{16}}$$

Subtract 4 from -\frac{9}{2} to get -\frac{17}{2}.

$$-\frac{17}{2}-\sqrt{\frac{25}{16}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$-\frac{17}{2}-\frac{5}{4}$$

Subtract \frac{5}{4} from -\frac{17}{2} to get -\frac{39}{4}.

$$-\frac{39}{4}$$

Factor

$$-\frac{39}{4} = -9\frac{3}{4} = -9.75$$