Calculus Examples

$2000 - 2000 {(\sqrt[3]{0.93})}^{30}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${\sqrt[3]{0.93}}^{30}$ as ${0.93}^{10}$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{0.93}$ as ${0.93}^{\frac{1}{3}}$ .

$2000 - 2000 {({0.93}^{\frac{1}{3}})}^{30}$

Step 1.1.2

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

$2000 - 2000 \cdot {0.93}^{\frac{1}{3} \cdot 30}$

Step 1.1.3

Combine $\frac{1}{3}$ and $30$ .

$2000 - 2000 \cdot {0.93}^{\frac{30}{3}}$

Step 1.1.4

Cancel the common factor of $30$ and $3$ .

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Step 1.1.4.1

Factor $3$ out of $30$ .

$2000 - 2000 \cdot {0.93}^{\frac{3 \cdot 10}{3}}$

Step 1.1.4.2

Cancel the common factors.

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Step 1.1.4.2.1

Factor $3$ out of $3$ .

$2000 - 2000 \cdot {0.93}^{\frac{3 \cdot 10}{3 (1)}}$

Step 1.1.4.2.2

Cancel the common factor.

$2000 - 2000 \cdot {0.93}^{\frac{3 \cdot 10}{3 \cdot 1}}$

Step 1.1.4.2.3

Rewrite the expression.

$2000 - 2000 \cdot {0.93}^{\frac{10}{1}}$

Step 1.1.4.2.4

Divide $10$ by $1$ .

$2000 - 2000 \cdot {0.93}^{10}$

Step 1.2

Raise $0.93$ to the power of $10$ .

$2000 - 2000 \cdot 0.4839823$

Step 1.3

Multiply $- 2000$ by $0.4839823$ .

$2000 - 967.96461435$

Step 2

Subtract $967.96461435$ from $2000$ .

$1032.03538564$