Basic Math Examples

$\frac{3 {(16)}^{2}}{16 + \sqrt{16}} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{3 \cdot 256}{16 + \sqrt{16}} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$\frac{3 \cdot 256}{16 + \sqrt{4^{2}}} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.2.2

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

$\frac{3 \cdot 256}{16 + 4} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.2.3

Add $16$ and $4$ .

$\frac{3 \cdot 256}{20} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.3

Multiply $3$ by $256$ .

$\frac{768}{20} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.4

Cancel the common factor of $768$ and $20$ .

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Step 1.4.1

Factor $4$ out of $768$ .

$\frac{4 (192)}{20} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $4$ out of $20$ .

$\frac{4 \cdot 192}{4 \cdot 5} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.4.2.2

Cancel the common factor.

$\frac{4 \cdot 192}{4 \cdot 5} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.4.2.3

Rewrite the expression.

$\frac{192}{5} - \frac{(\frac{1}{2 \cdot \sqrt{16}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.5

Simplify the denominator.

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Step 1.5.1

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

$\frac{192}{5} - \frac{(\frac{1}{2 \sqrt{4^{2}}} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.5.2

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

$\frac{192}{5} - \frac{(\frac{1}{2 \cdot 4} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.6

Multiply $2$ by $4$ .

$\frac{192}{5} - \frac{(\frac{1}{8} + 1) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

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

$\frac{192}{5} - \frac{(\frac{1}{8} + \frac{8}{8}) \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.7.2

Combine the numerators over the common denominator.

$\frac{192}{5} - \frac{\frac{1 + 8}{8} \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.7.3

Add $1$ and $8$ .

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 16^{3}}{{(16 + \sqrt{16})}^{2}}$

Step 1.7.4

Raise $16$ to the power of $3$ .

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 4096}{{(16 + \sqrt{16})}^{2}}$

Step 1.8

Simplify the denominator.

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Step 1.8.1

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

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 4096}{{(16 + \sqrt{4^{2}})}^{2}}$

Step 1.8.2

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

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 4096}{{(16 + 4)}^{2}}$

Step 1.8.3

Add $16$ and $4$ .

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 4096}{20^{2}}$

Step 1.8.4

Raise $20$ to the power of $2$ .

$\frac{192}{5} - \frac{\frac{9}{8} \cdot 4096}{400}$

Step 1.9

Combine $\frac{9}{8}$ and $4096$ .

$\frac{192}{5} - \frac{\frac{9 \cdot 4096}{8}}{400}$

Step 1.10

Multiply $9$ by $4096$ .

$\frac{192}{5} - \frac{\frac{36864}{8}}{400}$

Step 1.11

Divide $36864$ by $8$ .

$\frac{192}{5} - \frac{4608}{400}$

Step 1.12

Cancel the common factor of $4608$ and $400$ .

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Step 1.12.1

Factor $16$ out of $4608$ .

$\frac{192}{5} - \frac{16 (288)}{400}$

Step 1.12.2

Cancel the common factors.

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Step 1.12.2.1

Factor $16$ out of $400$ .

$\frac{192}{5} - \frac{16 \cdot 288}{16 \cdot 25}$

Step 1.12.2.2

Cancel the common factor.

$\frac{192}{5} - \frac{16 \cdot 288}{16 \cdot 25}$

Step 1.12.2.3

Rewrite the expression.

$\frac{192}{5} - \frac{288}{25}$

Step 2

To write $\frac{192}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{192}{5} \cdot \frac{5}{5} - \frac{288}{25}$

Step 3

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{192}{5}$ by $\frac{5}{5}$ .

$\frac{192 \cdot 5}{5 \cdot 5} - \frac{288}{25}$

Step 3.2

Multiply $5$ by $5$ .

$\frac{192 \cdot 5}{25} - \frac{288}{25}$

Step 4

Combine the numerators over the common denominator.

$\frac{192 \cdot 5 - 288}{25}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $192$ by $5$ .

$\frac{960 - 288}{25}$

Step 5.2

Subtract $288$ from $960$ .

$\frac{672}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{672}{25}$

Decimal Form:

$26.88$

Mixed Number Form:

$26 \frac{22}{25}$