Solve x^frac{4{5}}x^frac{-2{5}}x^frac{3{5}}

$$x ^ { \frac { 4 } { 5 } } x ^ { \frac { - 2 } { 5 } } x ^ { \frac { 3 } { 5 } }$$

Evaluate

$$x$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{\frac{4}{5}}x^{-\frac{2}{5}}x^{\frac{3}{5}}$$

Use the Multiplication Rule for Exponents.

$$x^{\frac{4-2+3}{5}}$$

Add the exponents \frac{4}{5} and -\frac{2}{5}.

$$x^{\frac{2+3}{5}}$$

Add the exponents \frac{2}{5} and \frac{3}{5}.

$$x^{1}$$

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

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{4}{5} and \frac{3}{5} to get \frac{7}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{7}{5}}x^{\frac{-2}{5}})$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{7}{5}}x^{-\frac{2}{5}})$$

To multiply powers of the same base, add their exponents. Add \frac{7}{5} and -\frac{2}{5} to get 1.

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

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$