Solve a*a^-frac{3{4}}*a^frac{1{4}}

$$a \cdot a ^ { - \frac { 3 } { 4 } } \cdot a ^ { \frac { 1 } { 4 } }$$

Evaluate

$$\sqrt{a}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{1}a^{-\frac{3}{4}}\sqrt[4]{a}$$

Use the Multiplication Rule for Exponents.

$$a^{1-\frac{3}{4}+\frac{1}{4}}$$

Add the exponents 1 and -\frac{3}{4}.

$$a^{\frac{1+1}{4}}$$

Add the exponents \frac{1}{4} and \frac{1}{4}.

$$\sqrt{a}$$

Differentiate w.r.t. a

$$\frac{1}{2\sqrt{a}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -\frac{3}{4} to get \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{1}{4}}a^{\frac{1}{4}})$$

To multiply powers of the same base, add their exponents. Add \frac{1}{4} and \frac{1}{4} to get \frac{1}{2}.

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

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

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

Subtract 1 from \frac{1}{2}.

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