Solve y9^5div9^-3

$$y 9 ^ { 5 } \div 9 ^ { - 3 }$$

Evaluate

$$43046721y$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$9^{8}y$$

Calculate 9 to the power of 8 and get 43046721.

$$43046721y$$

Differentiate w.r.t. y

$$43046721$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}y}(9^{8}y)$$

Calculate 9 to the power of 8 and get 43046721.

$$\frac{\mathrm{d}}{\mathrm{d}y}(43046721y)$$

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

$$43046721y^{1-1}$$

Subtract 1 from 1.

$$43046721y^{0}$$

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

$$43046721\times 1$$

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

$$43046721$$