Solve a^10/(a^3)^3

$$\frac { a ^ { 10 } } { ( a ^ { 3 } ) ^ { 3 } }$$

Evaluate

$$a$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{10}}{a^{9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 10 to get 1.

$$a^{1}$$

Calculate a to the power of 1 and get a.

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{a^{9}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 10 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{1})$$

Calculate a to the power of 1 and get a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

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

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

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

$$1$$