Solve frac{a^frac{3{2}}}{a^frac{1{2}}}

$$\frac { a ^ { \frac { 3 } { 2 } } } { a ^ { \frac { 1 } { 2 } } }$$

Evaluate

$$a$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$a^{\frac{3}{2}-\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{3}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$a^{1}$$

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

$$a$$

Differentiate w.r.t. a

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{\frac{3}{2}-\frac{1}{2}})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$a^{1-1}$$

Do the arithmetic.

$$a^{0}$$

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

$$1$$