Evaluate x^-1(x^-2+x^-3)

$x^{- 1} (x^{- 2} + x^{- 3})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify terms.

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x} (\frac{1}{x^{2}} + \frac{1}{x^{3}})$

Multiply $\frac{1}{x}$ by $\frac{1}{x^{2}} + \frac{1}{x^{3}}$ .

$\frac{\frac{1}{x^{2}} + \frac{1}{x^{3}}}{x}$

Step 3

Simplify the numerator.

To write $\frac{1}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\frac{1}{x^{2}} \cdot \frac{x}{x} + \frac{1}{x^{3}}}{x}$

Write each expression with a common denominator of $x^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x^{2}}$ by $\frac{x}{x}$ .

$\frac{\frac{x}{x^{2} x} + \frac{1}{x^{3}}}{x}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{\frac{x}{x^{2} x^{1}} + \frac{1}{x^{3}}}{x}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{x}{x^{2 + 1}} + \frac{1}{x^{3}}}{x}$

Add $2$ and $1$ .

$\frac{\frac{x}{x^{3}} + \frac{1}{x^{3}}}{x}$

Combine the numerators over the common denominator.

$\frac{\frac{x + 1}{x^{3}}}{x}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{x + 1}{x^{3}} \cdot \frac{1}{x}$

Step 5

Multiply $\frac{x + 1}{x^{3}} \cdot \frac{1}{x}$ .

Multiply $\frac{x + 1}{x^{3}}$ by $\frac{1}{x}$ .

$\frac{x + 1}{x^{3} x}$

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{x + 1}{x^{3} x^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x + 1}{x^{3 + 1}}$

Add $3$ and $1$ .

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