Solve 128^frac{-2{7}}-(625^-3)^frac{-1{4}}+14(2401)^frac{-1{4}}

$$128 ^ { \frac { - 2 } { 7 } } - ( 625 ^ { - 3 } ) ^ { \frac { - 1 } { 4 } } + 14 ( 2401 ) ^ { \frac { - 1 } { 4 } }$$

Evaluate

$$-\frac{491}{4}=-122.75$$

Solution Steps

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$128^{-\frac{2}{7}}-\left(625^{-3}\right)^{\frac{-1}{4}}+14\times 2401^{\frac{-1}{4}}$$

Calculate 128 to the power of -\frac{2}{7} and get \frac{1}{4}.

$$\frac{1}{4}-\left(625^{-3}\right)^{\frac{-1}{4}}+14\times 2401^{\frac{-1}{4}}$$

Calculate 625 to the power of -3 and get \frac{1}{244140625}.

$$\frac{1}{4}-\left(\frac{1}{244140625}\right)^{\frac{-1}{4}}+14\times 2401^{\frac{-1}{4}}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{1}{4}-\left(\frac{1}{244140625}\right)^{-\frac{1}{4}}+14\times 2401^{\frac{-1}{4}}$$

Calculate \frac{1}{244140625} to the power of -\frac{1}{4} and get 125.

$$\frac{1}{4}-125+14\times 2401^{\frac{-1}{4}}$$

Subtract 125 from \frac{1}{4} to get -\frac{499}{4}.

$$-\frac{499}{4}+14\times 2401^{\frac{-1}{4}}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{499}{4}+14\times 2401^{-\frac{1}{4}}$$

Calculate 2401 to the power of -\frac{1}{4} and get \frac{1}{7}.

$$-\frac{499}{4}+14\times \frac{1}{7}$$

Multiply 14 and \frac{1}{7} to get 2.

$$-\frac{499}{4}+2$$

Add -\frac{499}{4} and 2 to get -\frac{491}{4}.

$$-\frac{491}{4}$$

Factor

$$-\frac{491}{4} = -122\frac{3}{4} = -122.75$$