Solve {l}{sqrt{3^-2}*2^-4}{-6+(8-3)-[4+(6-3)*5-8]+3-{9-(6-4)}}

$$\left. \begin{array} { l } { \sqrt { 3 ^ { - 2 } } \cdot 2 ^ { - 4 } } \\ { - 6 + ( 8 - 3 ) - [ 4 + ( 6 - 3 ) * 5 - 8 ] + 3 - \{ 9 - ( 6 - 4 ) \} } \end{array} \right.$$

Evaluate

$$-\frac{767}{48}\approx -15.979166667$$

Solution Steps

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

$$\sqrt{\frac{1}{9}}\times 2^{-4}-6+8-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{3}\times 2^{-4}-6+8-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

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

$$\frac{1}{3}\times \frac{1}{16}-6+8-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Multiply \frac{1}{3} and \frac{1}{16} to get \frac{1}{48}.

$$\frac{1}{48}-6+8-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Subtract 6 from \frac{1}{48} to get -\frac{287}{48}.

$$-\frac{287}{48}+8-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Add -\frac{287}{48} and 8 to get \frac{97}{48}.

$$\frac{97}{48}-3-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Subtract 3 from \frac{97}{48} to get -\frac{47}{48}.

$$-\frac{47}{48}-\left(4+\left(6-3\right)\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Subtract 3 from 6 to get 3.

$$-\frac{47}{48}-\left(4+3\times 5-8\right)+3-\left(9-\left(6-4\right)\right)$$

Multiply 3 and 5 to get 15.

$$-\frac{47}{48}-\left(4+15-8\right)+3-\left(9-\left(6-4\right)\right)$$

Add 4 and 15 to get 19.

$$-\frac{47}{48}-\left(19-8\right)+3-\left(9-\left(6-4\right)\right)$$

Subtract 8 from 19 to get 11.

$$-\frac{47}{48}-11+3-\left(9-\left(6-4\right)\right)$$

Subtract 11 from -\frac{47}{48} to get -\frac{575}{48}.

$$-\frac{575}{48}+3-\left(9-\left(6-4\right)\right)$$

Add -\frac{575}{48} and 3 to get -\frac{431}{48}.

$$-\frac{431}{48}-\left(9-\left(6-4\right)\right)$$

Subtract 4 from 6 to get 2.

$$-\frac{431}{48}-\left(9-2\right)$$

Subtract 2 from 9 to get 7.

$$-\frac{431}{48}-7$$

Subtract 7 from -\frac{431}{48} to get -\frac{767}{48}.

$$-\frac{767}{48}$$

Factor

$$-\frac{767}{48} = -15\frac{47}{48} = -15.979166666666666$$