Finite Math Examples

$w (3000) = 2^{- \frac{3000}{24360}}$

Step 1

Cancel the common factor of $3000$ and $24360$ .

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Step 1.1

Factor $120$ out of $3000$ .

$w (3000) = 2^{- \frac{120 (25)}{24360}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $120$ out of $24360$ .

$w (3000) = 2^{- \frac{120 \cdot 25}{120 \cdot 203}}$

Step 1.2.2

Cancel the common factor.

$w (3000) = 2^{- \frac{120 \cdot 25}{120 \cdot 203}}$

Step 1.2.3

Rewrite the expression.

$w (3000) = 2^{- \frac{25}{203}}$

Step 2

Divide each term in $w (3000) = 2^{- \frac{25}{203}}$ by $3000$ and simplify.

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Step 2.1

Divide each term in $w (3000) = 2^{- \frac{25}{203}}$ by $3000$ .

$\frac{w (3000)}{3000} = \frac{2^{- \frac{25}{203}}}{3000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{w \cdot 3000}{3000} = \frac{2^{- \frac{25}{203}}}{3000}$

Step 2.2.1.2

Divide $w$ by $1$ .

$w = \frac{2^{- \frac{25}{203}}}{3000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move $2^{- \frac{25}{203}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$w = \frac{1}{3000 \cdot 2^{\frac{25}{203}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$w = \frac{1}{3000 \cdot 2^{\frac{25}{203}}}$

Decimal Form:

$w = 0.00030605 \dots$