Basic Math Examples

$1 + 2^{3 - \sqrt{36}} \div 2 + 4$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite the division as a fraction.

$1 + \frac{2^{3 - \sqrt{36}}}{2} + 4$

Step 1.2

Move $2^{3 - \sqrt{36}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 + \frac{1}{2 \cdot 2^{- (3 - \sqrt{36})}} + 4$

Step 1.3

Multiply $2$ by $2^{- (3 - \sqrt{36})}$ by adding the exponents.

Tap for more steps...

Step 1.3.1

Multiply $2$ by $2^{- (3 - \sqrt{36})}$ .

Tap for more steps...

Step 1.3.1.1

Raise $2$ to the power of $1$ .

$1 + \frac{1}{2^{1} \cdot 2^{- (3 - \sqrt{36})}} + 4$

Step 1.3.1.2

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

$1 + \frac{1}{2^{1 - (3 - \sqrt{36})}} + 4$

Step 1.3.2

Simplify each term.

Tap for more steps...

Step 1.3.2.1

Rewrite $36$ as $6^{2}$ .

$1 + \frac{1}{2^{1 - (3 - \sqrt{6^{2}})}} + 4$

Step 1.3.2.2

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

$1 + \frac{1}{2^{1 - (3 - 1 \cdot 6)}} + 4$

Step 1.3.2.3

Multiply $- 1$ by $6$ .

$1 + \frac{1}{2^{1 - (3 - 6)}} + 4$

Step 1.3.3

Subtract $6$ from $3$ .

$1 + \frac{1}{2^{1 - - 3}} + 4$

Step 1.3.4

Multiply $- 1$ by $- 3$ .

$1 + \frac{1}{2^{1 + 3}} + 4$

Step 1.3.5

Add $1$ and $3$ .

$1 + \frac{1}{2^{4}} + 4$

Step 1.4

Raise $2$ to the power of $4$ .

$1 + \frac{1}{16} + 4$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Write $1$ as a fraction with denominator $1$ .

$\frac{1}{1} + \frac{1}{16} + 4$

Step 2.2

Multiply $\frac{1}{1}$ by $\frac{16}{16}$ .

$\frac{1}{1} \cdot \frac{16}{16} + \frac{1}{16} + 4$

Step 2.3

Multiply $\frac{1}{1}$ by $\frac{16}{16}$ .

$\frac{16}{16} + \frac{1}{16} + 4$

Step 2.4

Write $4$ as a fraction with denominator $1$ .

$\frac{16}{16} + \frac{1}{16} + \frac{4}{1}$

Step 2.5

Multiply $\frac{4}{1}$ by $\frac{16}{16}$ .

$\frac{16}{16} + \frac{1}{16} + \frac{4}{1} \cdot \frac{16}{16}$

Step 2.6

Multiply $\frac{4}{1}$ by $\frac{16}{16}$ .

$\frac{16}{16} + \frac{1}{16} + \frac{4 \cdot 16}{16}$

Step 3

Combine the numerators over the common denominator.

$\frac{16 + 1 + 4 \cdot 16}{16}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Multiply $4$ by $16$ .

$\frac{16 + 1 + 64}{16}$

Step 4.2

Add $16$ and $1$ .

$\frac{17 + 64}{16}$

Step 4.3

Add $17$ and $64$ .

$\frac{81}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{16}$

Decimal Form:

$5.0625$

Mixed Number Form:

$5 \frac{1}{16}$