Calculus Examples

$16^{\sqrt{16}} (\frac{2 + \ln (16)}{2 \sqrt{16}})$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Rewrite $16$ as $4^{2}$ .

$16^{\sqrt{4^{2}}} \frac{2 + \ln (16)}{2 \sqrt{16}}$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$16^{4} \frac{2 + \ln (16)}{2 \sqrt{16}}$

Step 1.3

Raise $16$ to the power of $4$ .

$65536 \frac{2 + \ln (16)}{2 \sqrt{16}}$

Step 2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1

Simplify the denominator.

Tap for more steps...

Step 2.1.1

Rewrite $16$ as $4^{2}$ .

$65536 \frac{2 + \ln (16)}{2 \sqrt{4^{2}}}$

Step 2.1.2

Pull terms out from under the radical, assuming positive real numbers.

$65536 \frac{2 + \ln (16)}{2 \cdot 4}$

Step 2.2

Multiply $2$ by $4$ .

$65536 \frac{2 + \ln (16)}{8}$

Step 2.3

Factor $2$ out of $65536$ .

$2 (32768) \frac{2 + \ln (16)}{8}$

Step 2.4

Factor $2$ out of $8$ .

$2 \cdot 32768 \frac{2 + \ln (16)}{2 \cdot 4}$

Step 2.5

Cancel the common factor.

$2 \cdot 32768 \frac{2 + \ln (16)}{2 \cdot 4}$

Step 2.6

Rewrite the expression.

$32768 \frac{2 + \ln (16)}{4}$

Step 3

Combine $32768$ and $\frac{2 + \ln (16)}{4}$ .

$\frac{32768 (2 + \ln (16))}{4}$

Step 4

Cancel the common factor of $32768$ and $4$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $32768 (2 + \ln (16))$ .

$\frac{4 (8192 (2 + \ln (16)))}{4}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $4$ out of $4$ .

$\frac{4 (8192 (2 + \ln (16)))}{4 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{4 (8192 (2 + \ln (16)))}{4 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{8192 (2 + \ln (16))}{1}$

Step 4.2.4

Divide $8192 (2 + \ln (16))$ by $1$ .

$8192 (2 + \ln (16))$

Step 5

Apply the distributive property.

$8192 \cdot 2 + 8192 \ln (16)$

Step 6

Multiply $8192$ by $2$ .

$16384 + 8192 \ln (16)$

Step 7

The result can be shown in multiple forms.

Exact Form:

$16384 + 8192 \ln (16)$

Decimal Form:

$39097.04681258 \dots$