Solve E_{J}:5^7/5^4=

$$E _ { J } : \frac { 5 ^ { 7 } } { 5 ^ { 4 } } =$$

Evaluate

$$\frac{E_{J}}{125}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$\frac{E_{J}}{5^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{E_{J}}{125}$$

Differentiate w.r.t. E_J

$$\frac{1}{125} = 0.008$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}E_{J}}(\frac{E_{J}}{5^{3}})$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\mathrm{d}}{\mathrm{d}E_{J}}(\frac{E_{J}}{125})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{125}E_{J}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{125}E_{J}^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{125}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{125}$$