Solve 3^6*a^5/9^2*a^3

$$\frac { 3 ^ { 6 } \times a ^ { 5 } } { 9 ^ { 2 } \times a ^ { 3 } }$$

Evaluate

$$9a^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{3^{6}a^{5}}{9^{2}a^{3}}$$

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

$$\frac{3^{6}a^{5-3}}{9^{2}}$$

Subtract 3 from 5.

$$\frac{3^{6}a^{2}}{9^{2}}$$

Raise 3 to the power 6.

$$\frac{729a^{2}}{9^{2}}$$

Raise 9 to the power 2.

$$\frac{729a^{2}}{81}$$

Divide 729 by 81.

$$9a^{2}$$

Differentiate w.r.t. a

$$18a$$

Steps Using Definition of a Derivative

Cancel out a^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3^{6}a^{2}}{9^{2}})$$

Calculate 3 to the power of 6 and get 729.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{729a^{2}}{9^{2}})$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{729a^{2}}{81})$$

Divide 729a^{2} by 81 to get 9a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{2})$$

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

$$2\times 9a^{2-1}$$

Multiply 2 times 9.

$$18a^{2-1}$$

Subtract 1 from 2.

$$18a^{1}$$

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

$$18a$$