Solve [-7/8]^-7:[49/512]

$$[ \frac { - 7 } { 8 } ] ^ { - 7 } : [ \frac { 49 } { 512 } ]$$

Evaluate

$$-\frac{1073741824}{40353607}\approx -26.608323365$$

Solution Steps

Fraction \frac{-7}{8} can be rewritten as -\frac{7}{8} by extracting the negative sign.

$$\frac{\left(-\frac{7}{8}\right)^{-7}}{\frac{49}{512}}$$

Calculate -\frac{7}{8} to the power of -7 and get -\frac{2097152}{823543}.

$$\frac{-\frac{2097152}{823543}}{\frac{49}{512}}$$

Divide -\frac{2097152}{823543} by \frac{49}{512} by multiplying -\frac{2097152}{823543} by the reciprocal of \frac{49}{512}.

$$-\frac{2097152}{823543}\times \frac{512}{49}$$

Multiply -\frac{2097152}{823543} and \frac{512}{49} to get -\frac{1073741824}{40353607}.

$$-\frac{1073741824}{40353607}$$

Factor

$$-\frac{1073741824}{40353607} = -26\frac{24548042}{40353607} = -26.60832336499684$$