Solve (a^2)^3diva^5

$$( a ^ { 2 } ) ^ { 3 } \div a ^ { 5 }$$

Evaluate

$$a$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(a^{2}\right)^{3}\times \frac{1}{a^{5}}$$

To raise a power to another power, multiply the exponents.

$$a^{2\times 3}a^{5\left(-1\right)}$$

Multiply 2 times 3.

$$a^{6}a^{5\left(-1\right)}$$

Multiply 5 times -1.

$$a^{6}a^{-5}$$

To multiply powers of the same base, add their exponents.

$$a^{6-5}$$

Add the exponents 6 and -5.

$$a^{1}$$

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

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}}{a^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 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.

$$1$$