Simplify (x^(2n)*x^(3n-1))/(x^(n+2))

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

Step 1

Multiply $x^{2 n}$ by $x^{3 n - 1}$ by adding the exponents.

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

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

Add $2 n$ and $3 n$ .

$\frac{x^{5 n - 1}}{x^{n + 2}}$

Step 2

Cancel the common factor of $x^{5 n - 1}$ and $x^{n + 2}$ .

Factor $x^{n + 2}$ out of $x^{5 n - 1}$ .

$\frac{x^{n + 2} x^{5 n - 1 - (n + 2)}}{x^{n + 2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{n + 2} x^{5 n - 1 - (n + 2)}}{x^{n + 2} \cdot 1}$

Cancel the common factor.

$\frac{x^{n + 2} x^{5 n - 1 - (n + 2)}}{x^{n + 2} \cdot 1}$

Rewrite the expression.

$\frac{x^{5 n - 1 - (n + 2)}}{1}$

Divide $x^{5 n - 1 - (n + 2)}$ by $1$ .

$x^{5 n - 1 - (n + 2)}$

Step 3

Simplify each term.

Apply the distributive property.

$x^{5 n - 1 - n - 1 \cdot 2}$

Multiply $- 1$ by $2$ .

$x^{5 n - 1 - n - 2}$

Step 4

Simplify by adding terms.

Subtract $n$ from $5 n$ .

$x^{4 n - 1 - 2}$

Subtract $2$ from $- 1$ .

$x^{4 n - 3}$