Finite Math Examples

$20 {(\frac{1}{2})}^{19} {(\frac{1}{2})}^{20 - 19}$

Step 1

Multiply ${(\frac{1}{2})}^{19}$ by ${(\frac{1}{2})}^{20 - 19}$ by adding the exponents.

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Step 1.1

Move ${(\frac{1}{2})}^{20 - 19}$ .

$20 ({(\frac{1}{2})}^{20 - 19} {(\frac{1}{2})}^{19})$

Step 1.2

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

$20 {(\frac{1}{2})}^{20 - 19 + 19}$

Step 1.3

Subtract $19$ from $20$ .

$20 {(\frac{1}{2})}^{1 + 19}$

Step 1.4

Add $1$ and $19$ .

$20 {(\frac{1}{2})}^{20}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{1}{2}$ .

$20 \frac{1^{20}}{2^{20}}$

Step 2.2

One to any power is one.

$20 \frac{1}{2^{20}}$

Step 2.3

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

$20 (\frac{1}{1048576})$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $20$ .

$4 (5) \frac{1}{1048576}$

Step 3.2

Factor $4$ out of $1048576$ .

$4 \cdot 5 \frac{1}{4 \cdot 262144}$

Step 3.3

Cancel the common factor.

$4 \cdot 5 \frac{1}{4 \cdot 262144}$

Step 3.4

Rewrite the expression.

$5 (\frac{1}{262144})$

Step 4

Combine $5$ and $\frac{1}{262144}$ .

$\frac{5}{262144}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{262144}$

Decimal Form:

$1.90734863 \cdot 10^{- 5}$