Simplify 5/(4n)*10/(2n)

$\frac{5}{4 n} \cdot \frac{10}{2 n}$

Step 1

Cancel the common factor of $2$ .

Factor $2$ out of $4 n$ .

$\frac{5}{2 (2 n)} \cdot \frac{10}{2 n}$

Factor $2$ out of $10$ .

$\frac{5}{2 (2 n)} \cdot \frac{2 (5)}{2 n}$

Cancel the common factor.

$\frac{5}{2 (2 n)} \cdot \frac{2 \cdot 5}{2 n}$

Rewrite the expression.

$\frac{5}{2 n} \cdot \frac{5}{2 n}$

Step 2

Multiply $\frac{5}{2 n}$ by $\frac{5}{2 n}$ .

$\frac{5 \cdot 5}{2 n (2 n)}$

Step 3

Multiply.

Multiply $5$ by $5$ .

$\frac{25}{2 n (2 n)}$

Multiply $2$ by $2$ .

$\frac{25}{4 n \cdot n}$

Step 4

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

$\frac{25}{4 (n^{1} n)}$

Step 5

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

$\frac{25}{4 (n^{1} n^{1})}$

Step 6

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

$\frac{25}{4 n^{1 + 1}}$

Step 7

Add $1$ and $1$ .

$\frac{25}{4 n^{2}}$