Finite Math Examples

$y = 2000 (2^{- 0.2 \cdot 10})$

Step 1

Multiply $2000$ by $2^{- 0.2 \cdot 10}$ .

$y = 2000 \cdot 2^{- 0.2 \cdot 10}$

Step 2

Simplify $2000 \cdot 2^{- 0.2 \cdot 10}$ .

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Step 2.1

Multiply $- 0.2$ by $10$ .

$y = 2000 \cdot 2^{- 2}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = 2000 \cdot \frac{1}{2^{2}}$

Step 2.3

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

$y = 2000 \cdot \frac{1}{4}$

Step 2.4

Cancel the common factor of $4$ .

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Step 2.4.1

Factor $4$ out of $2000$ .

$y = 4 (500) \cdot \frac{1}{4}$

Step 2.4.2

Cancel the common factor.

$y = 4 \cdot 500 \cdot \frac{1}{4}$

Step 2.4.3

Rewrite the expression.

$y = 500$