Basic Math Examples

$\frac{e^{36} + 1}{4}$

Step 1

Rewrite $e^{36}$ as ${(e^{12})}^{3}$ .

$\frac{{(e^{12})}^{3} + 1}{4}$

Step 2

Rewrite $1$ as $1^{3}$ .

$\frac{{(e^{12})}^{3} + 1^{3}}{4}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = e^{12}$ and $b = 1$ .

$\frac{(e^{12} + 1) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Rewrite $e^{12}$ as ${(e^{4})}^{3}$ .

$\frac{({(e^{4})}^{3} + 1) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.2

Rewrite $1$ as $1^{3}$ .

$\frac{({(e^{4})}^{3} + 1^{3}) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = e^{4}$ and $b = 1$ .

$\frac{(e^{4} + 1) ({(e^{4})}^{2} - e^{4} \cdot 1 + 1^{2}) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.4

Simplify.

Tap for more steps...

Step 4.4.1

Multiply the exponents in ${(e^{4})}^{2}$ .

Tap for more steps...

Step 4.4.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(e^{4} + 1) (e^{4 \cdot 2} - e^{4} \cdot 1 + 1^{2}) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.4.1.2

Multiply $4$ by $2$ .

$\frac{(e^{4} + 1) (e^{8} - e^{4} \cdot 1 + 1^{2}) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.4.2

Multiply $- 1$ by $1$ .

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1^{2}) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.4.3

One to any power is one.

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) ({(e^{12})}^{2} - e^{12} \cdot 1 + 1^{2})}{4}$

Step 4.5

Multiply $- 1$ by $1$ .

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) ({(e^{12})}^{2} - e^{12} + 1^{2})}{4}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Multiply the exponents in ${(e^{12})}^{2}$ .

Tap for more steps...

Step 5.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) (e^{12 \cdot 2} - e^{12} + 1^{2})}{4}$

Step 5.1.2

Multiply $12$ by $2$ .

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) (e^{24} - e^{12} + 1^{2})}{4}$

Step 5.2

One to any power is one.

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) (e^{24} - e^{12} + 1)}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{(e^{4} + 1) (e^{8} - e^{4} + 1) (e^{24} - e^{12} + 1)}{4}$

Decimal Form:

$1.07780788 \cdot 10^{15}$