Solve b5^7/5^4

$$b \frac { 5 ^ { 7 } } { 5 ^ { 4 } }$$

Evaluate

$$125b$$

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.

$$b\times 5^{3}$$

Calculate 5 to the power of 3 and get 125.

$$b\times 125$$

Differentiate w.r.t. b

$$125$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\times 5^{3})$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\times 125)$$

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

$$125b^{1-1}$$

Subtract 1 from 1.

$$125b^{0}$$

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

$$125\times 1$$

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

$$125$$