Solve a^8:a^5/a^3:a^2

$$\frac { a ^ { 8 } : a ^ { 5 } } { a ^ { 3 } : a ^ { 2 } }$$

Evaluate

$$a^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 8 to get 3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\frac{a^{3}}{a^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 8 to get 3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{3}}{a^{1}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 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.

$$2a$$