Calculus Examples

$2000 = - 18000 {(0 + 64)}^{- \frac{1}{2}} + c$

Step 1

Rewrite the equation as $- 18000 {(0 + 64)}^{- \frac{1}{2}} + c = 2000$ .

$- 18000 {(0 + 64)}^{- \frac{1}{2}} + c = 2000$

Step 2

Simplify $- 18000 {(0 + 64)}^{- \frac{1}{2}} + c$ .

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Step 2.1

Add $0$ and $64$ .

$- 18000 \cdot 64^{- \frac{1}{2}} + c = 2000$

Step 2.2

Simplify each term.

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Step 2.2.1

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

$- 18000 \cdot \frac{1}{64^{\frac{1}{2}}} + c = 2000$

Step 2.2.2

Simplify the denominator.

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Step 2.2.2.1

Rewrite $64$ as $8^{2}$ .

$- 18000 \cdot \frac{1}{{(8^{2})}^{\frac{1}{2}}} + c = 2000$

Step 2.2.2.2

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

$- 18000 \cdot \frac{1}{8^{2 (\frac{1}{2})}} + c = 2000$

Step 2.2.2.3

Cancel the common factor of $2$ .

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Step 2.2.2.3.1

Cancel the common factor.

$- 18000 \cdot \frac{1}{8^{2 (\frac{1}{2})}} + c = 2000$

Step 2.2.2.3.2

Rewrite the expression.

$- 18000 \cdot \frac{1}{8^{1}} + c = 2000$

Step 2.2.2.4

Evaluate the exponent.

$- 18000 \cdot \frac{1}{8} + c = 2000$

Step 2.2.3

Cancel the common factor of $8$ .

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Step 2.2.3.1

Factor $8$ out of $- 18000$ .

$8 (- 2250) \cdot \frac{1}{8} + c = 2000$

Step 2.2.3.2

Cancel the common factor.

$8 \cdot - 2250 \cdot \frac{1}{8} + c = 2000$

Step 2.2.3.3

Rewrite the expression.

$- 2250 + c = 2000$

Step 3

Move all terms not containing $c$ to the right side of the equation.

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Step 3.1

Add $2250$ to both sides of the equation.

$c = 2000 + 2250$

Step 3.2

Add $2000$ and $2250$ .

$c = 4250$