Basic Math Examples

$\frac{16^{2} \cdot 15^{3} \cdot 5^{2}}{{(40)}^{6} \cdot 3^{2}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Raise $16$ to the power of $2$ .

$\frac{256 \cdot 15^{3} \cdot 5^{2}}{40^{6} \cdot 3^{2}}$

Step 1.2

Raise $15$ to the power of $3$ .

$\frac{256 \cdot 3375 \cdot 5^{2}}{40^{6} \cdot 3^{2}}$

Step 1.3

Raise $5$ to the power of $2$ .

$\frac{256 \cdot 3375 \cdot 25}{40^{6} \cdot 3^{2}}$

Step 1.4

Combine exponents.

Tap for more steps...

Step 1.4.1

Multiply $256$ by $3375$ .

$\frac{864000 \cdot 25}{40^{6} \cdot 3^{2}}$

Step 1.4.2

Multiply $864000$ by $25$ .

$\frac{21600000}{40^{6} \cdot 3^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Raise $40$ to the power of $6$ .

$\frac{21600000}{4096000000 \cdot 3^{2}}$

Step 2.2

Raise $3$ to the power of $2$ .

$\frac{21600000}{4096000000 \cdot 9}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Multiply $4096000000$ by $9$ .

$\frac{21600000}{36864000000}$

Step 3.2

Cancel the common factor of $21600000$ and $36864000000$ .

Tap for more steps...

Step 3.2.1

Factor $7200000$ out of $21600000$ .

$\frac{7200000 (3)}{36864000000}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $7200000$ out of $36864000000$ .

$\frac{7200000 \cdot 3}{7200000 \cdot 5120}$

Step 3.2.2.2

Cancel the common factor.

$\frac{7200000 \cdot 3}{7200000 \cdot 5120}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3}{5120}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5120}$

Decimal Form:

$0.00058593 \dots$