Solve a^3*a^7/(a^2)^4

$$\frac { a ^ { 3 } \times a ^ { 7 } } { ( a ^ { 2 } ) ^ { 4 } }$$

Evaluate

$$a^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{a^{10}}{\left(a^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{a^{10}}{a^{8}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 10 to get 2.

$$a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{\left(a^{2}\right)^{4}})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{a^{8}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 10 to get 2.

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

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

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

Subtract 1 from 2.

$$2a^{1}$$

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

$$2a$$