Solve x^3*{left(-1/xright)}^2

$${ x }^{ 3 } \times { \left(- \frac{ 1 }{ x } \right) }^{ 2 }$$

Evaluate

$$x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(x^{1}\right)^{3}\left(-\frac{1}{x}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{3}\left(x^{1}\right)^{3}\times \left(\frac{1}{x}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$1^{3}x^{3}x^{-2}$$

To multiply powers of the same base, add their exponents.

$$1^{3}x^{3-2}$$

Add the exponents 3 and -2.

$$1^{3}x^{1}$$

Raise -1 to the power 2.

$$x^{1}$$

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

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Calculate -\frac{1}{x} to the power of 2 and get \left(\frac{1}{x}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times \left(\frac{1}{x}\right)^{2})$$

To raise \frac{1}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times \frac{1^{2}}{x^{2}})$$

Express x^{3}\times \frac{1^{2}}{x^{2}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}\times 1^{2}}{x^{2}})$$

Cancel out x^{2} in both numerator and denominator.

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

Calculate 1 to the power of 2 and get 1.

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

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.

$$1$$