Solve (-1/2x)^7div(-1/2)^1

$$( - \frac { 1 } { 2 } x ) ^ { 7 } \div ( - \frac { 1 } { 2 } ) ^ { 1 }$$

Evaluate

$$\frac{x^{7}}{64}$$

Solution Steps

Expand \left(-\frac{1}{2}x\right)^{7}.

$$\frac{\left(-\frac{1}{2}\right)^{7}x^{7}}{\left(-\frac{1}{2}\right)^{1}}$$

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

$$\frac{-\frac{1}{128}x^{7}}{\left(-\frac{1}{2}\right)^{1}}$$

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

$$\frac{-\frac{1}{128}x^{7}}{-\frac{1}{2}}$$

Divide -\frac{1}{128}x^{7} by -\frac{1}{2} by multiplying -\frac{1}{128}x^{7} by the reciprocal of -\frac{1}{2}.

$$\frac{-\frac{1}{128}x^{7}\times 2}{-1}$$

Anything divided by -1 gives its opposite.

$$\frac{1}{128}x^{7}\times 2$$

Multiply \frac{1}{128} and 2 to get \frac{1}{64}.

$$\frac{1}{64}x^{7}$$

Expand

$$\frac{x^{7}}{64}$$

Solution Steps

Expand \left(-\frac{1}{2}x\right)^{7}.

$$\frac{\left(-\frac{1}{2}\right)^{7}x^{7}}{\left(-\frac{1}{2}\right)^{1}}$$

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

$$\frac{-\frac{1}{128}x^{7}}{\left(-\frac{1}{2}\right)^{1}}$$

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

$$\frac{-\frac{1}{128}x^{7}}{-\frac{1}{2}}$$

Divide -\frac{1}{128}x^{7} by -\frac{1}{2} by multiplying -\frac{1}{128}x^{7} by the reciprocal of -\frac{1}{2}.

$$\frac{-\frac{1}{128}x^{7}\times 2}{-1}$$

Anything divided by -1 gives its opposite.

$$\frac{1}{128}x^{7}\times 2$$

Multiply \frac{1}{128} and 2 to get \frac{1}{64}.

$$\frac{1}{64}x^{7}$$