Pre-Algebra Examples

$\frac{7 n}{24 n^{3} - 64 n^{2}} \cdot \frac{9 n - 24}{7 n}$

Step 1

Factor $8 n^{2}$ out of $24 n^{3} - 64 n^{2}$ .

Tap for more steps...

Step 1.1

Factor $8 n^{2}$ out of $24 n^{3}$ .

$\frac{7 n}{8 n^{2} (3 n) - 64 n^{2}} \cdot \frac{9 n - 24}{7 n}$

Step 1.2

Factor $8 n^{2}$ out of $- 64 n^{2}$ .

$\frac{7 n}{8 n^{2} (3 n) + 8 n^{2} (- 8)} \cdot \frac{9 n - 24}{7 n}$

Step 1.3

Factor $8 n^{2}$ out of $8 n^{2} (3 n) + 8 n^{2} (- 8)$ .

$\frac{7 n}{8 n^{2} (3 n - 8)} \cdot \frac{9 n - 24}{7 n}$

Step 2

Factor $3$ out of $9 n - 24$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $9 n$ .

$\frac{7 n}{8 n^{2} (3 n - 8)} \cdot \frac{3 (3 n) - 24}{7 n}$

Step 2.2

Factor $3$ out of $- 24$ .

$\frac{7 n}{8 n^{2} (3 n - 8)} \cdot \frac{3 (3 n) + 3 (- 8)}{7 n}$

Step 2.3

Factor $3$ out of $3 (3 n) + 3 (- 8)$ .

$\frac{7 n}{8 n^{2} (3 n - 8)} \cdot \frac{3 (3 n - 8)}{7 n}$

Step 3

Combine.

$\frac{7 n (3 (3 n - 8))}{8 n^{2} (3 n - 8) (7 n)}$

Step 4

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

Tap for more steps...

Step 4.1

Move $n$ .

$\frac{7 n (3 (3 n - 8))}{8 (n \cdot n^{2}) (3 n - 8) \cdot 7}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{7 n (3 (3 n - 8))}{8 (n^{1} n^{2}) (3 n - 8) \cdot 7}$

Step 4.2.2

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

$\frac{7 n (3 (3 n - 8))}{8 n^{1 + 2} (3 n - 8) \cdot 7}$

Step 4.3

Add $1$ and $2$ .

$\frac{7 n (3 (3 n - 8))}{8 n^{3} (3 n - 8) \cdot 7}$

Step 5

Cancel the common factor of $7$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{7 n (3 (3 n - 8))}{8 n^{3} (3 n - 8) \cdot 7}$

Step 5.2

Rewrite the expression.

$\frac{n (3 (3 n - 8))}{8 n^{3} (3 n - 8)}$

Step 6

Cancel the common factors.

Tap for more steps...

Step 6.1

Factor $n$ out of $8 n^{3} (3 n - 8)$ .

$\frac{n (3 (3 n - 8))}{n (8 n^{2} (3 n - 8))}$

Step 6.2

Cancel the common factor.

$\frac{n (3 (3 n - 8))}{n (8 n^{2} (3 n - 8))}$

Step 6.3

Rewrite the expression.

$\frac{3 (3 n - 8)}{8 n^{2} (3 n - 8)}$

Step 7

Cancel the common factor of $3 n - 8$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{3 (3 n - 8)}{8 n^{2} (3 n - 8)}$

Step 7.2

Rewrite the expression.

$\frac{3}{8 n^{2}}$