Basic Math Examples

$(\frac{4^{2}}{5}) \cdot (\frac{4}{5}) \cdot (\frac{4^{5}}{5})$

Step 1

Raise $4$ to the power of $5$ .

$(\frac{4^{2}}{5}) \cdot (\frac{4}{5}) \cdot \frac{1024}{5}$

Step 2

Combine.

$\frac{4^{2} \cdot 4}{5 \cdot 5} \cdot \frac{1024}{5}$

Step 3

Combine.

$\frac{4^{2} \cdot 4 \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 4

Multiply $4^{2}$ by $4$ by adding the exponents.

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Step 4.1

Multiply $4^{2}$ by $4$ .

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Step 4.1.1

Raise $4$ to the power of $1$ .

$\frac{4^{2} \cdot 4^{1} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 4.1.2

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

$\frac{4^{2 + 1} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 4.2

Add $2$ and $1$ .

$\frac{4^{3} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{{(2^{2})}^{3} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 5.2

Multiply the exponents in ${(2^{2})}^{3}$ .

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Step 5.2.1

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

$\frac{2^{2 \cdot 3} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 5.2.2

Multiply $2$ by $3$ .

$\frac{2^{6} \cdot 1024}{5 \cdot 5 \cdot 5}$

Step 5.3

Rewrite $1024$ as $2^{10}$ .

$\frac{2^{6} \cdot 2^{10}}{5 \cdot 5 \cdot 5}$

Step 5.4

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

$\frac{2^{6 + 10}}{5 \cdot 5 \cdot 5}$

Step 5.5

Add $6$ and $10$ .

$\frac{2^{16}}{5 \cdot 5 \cdot 5}$

Step 6

Simplify the denominator.

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Step 6.1

Multiply $5$ by $5$ .

$\frac{2^{16}}{25 \cdot 5}$

Step 6.2

Multiply $25$ by $5$ .

$\frac{2^{16}}{125}$

Step 7

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

$\frac{65536}{125}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{65536}{125}$

Decimal Form:

$524.288$

Mixed Number Form:

$524 \frac{36}{125}$