Solve d/d2(2^3/2-2^7/7)=

$$\frac { d } { d 2 } ( \frac { 2 ^ { 3 } } { 2 } - \frac { 2 ^ { 7 } } { 7 } ) =$$

Evaluate

$$-\frac{100d}{7d_{2}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\frac{d}{d_{2}}\left(2^{2}-\frac{2^{7}}{7}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{d}{d_{2}}\left(4-\frac{2^{7}}{7}\right)$$

Calculate 2 to the power of 7 and get 128.

$$\frac{d}{d_{2}}\left(4-\frac{128}{7}\right)$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{d}{d_{2}}\left(\frac{28}{7}-\frac{128}{7}\right)$$

Since \frac{28}{7} and \frac{128}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{d}{d_{2}}\times \frac{28-128}{7}$$

Subtract 128 from 28 to get -100.

$$\frac{d}{d_{2}}\left(-\frac{100}{7}\right)$$

Multiply \frac{d}{d_{2}} times -\frac{100}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-d\times 100}{d_{2}\times 7}$$

Multiply -1 and 100 to get -100.

$$\frac{-100d}{d_{2}\times 7}$$

Expand

$$-\frac{100d}{7d_{2}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\frac{d}{d_{2}}\left(2^{2}-\frac{2^{7}}{7}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{d}{d_{2}}\left(4-\frac{2^{7}}{7}\right)$$

Calculate 2 to the power of 7 and get 128.

$$\frac{d}{d_{2}}\left(4-\frac{128}{7}\right)$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{d}{d_{2}}\left(\frac{28}{7}-\frac{128}{7}\right)$$

Since \frac{28}{7} and \frac{128}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{d}{d_{2}}\times \frac{28-128}{7}$$

Subtract 128 from 28 to get -100.

$$\frac{d}{d_{2}}\left(-\frac{100}{7}\right)$$

Multiply \frac{d}{d_{2}} times -\frac{100}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-d\times 100}{d_{2}\times 7}$$

Multiply -1 and 100 to get -100.

$$\frac{-100d}{d_{2}\times 7}$$