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

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

Evaluate

$$-\frac{27}{4}=-6.75$$

Solution Steps

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$-\frac{1}{256}\times \left(\frac{3^{-1}}{4}\right)^{-3}$$

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

$$-\frac{1}{256}\times \left(\frac{\frac{1}{3}}{4}\right)^{-3}$$

Express \frac{\frac{1}{3}}{4} as a single fraction.

$$-\frac{1}{256}\times \left(\frac{1}{3\times 4}\right)^{-3}$$

Multiply 3 and 4 to get 12.

$$-\frac{1}{256}\times \left(\frac{1}{12}\right)^{-3}$$

Calculate \frac{1}{12} to the power of -3 and get 1728.

$$-\frac{1}{256}\times 1728$$

Multiply -\frac{1}{256} and 1728 to get -\frac{27}{4}.

$$-\frac{27}{4}$$

Factor

$$-\frac{27}{4} = -6\frac{3}{4} = -6.75$$