Calculus Examples

$523 {(\frac{1}{2})}^{\frac{20}{30}}$

Step 1

Cancel the common factor of $20$ and $30$ .

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Step 1.1

Factor $10$ out of $20$ .

$523 {(\frac{1}{2})}^{\frac{10 (2)}{30}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $10$ out of $30$ .

$523 {(\frac{1}{2})}^{\frac{10 \cdot 2}{10 \cdot 3}}$

Step 1.2.2

Cancel the common factor.

$523 {(\frac{1}{2})}^{\frac{10 \cdot 2}{10 \cdot 3}}$

Step 1.2.3

Rewrite the expression.

$523 {(\frac{1}{2})}^{\frac{2}{3}}$

Step 2

Simplify the expression.

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Step 2.1

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

$523 \frac{1^{\frac{2}{3}}}{2^{\frac{2}{3}}}$

Step 2.2

One to any power is one.

$523 \frac{1}{2^{\frac{2}{3}}}$

Step 3

Combine $523$ and $\frac{1}{2^{\frac{2}{3}}}$ .

$\frac{523}{2^{\frac{2}{3}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{523}{2^{\frac{2}{3}}}$

Decimal Form:

$329.46935454 \dots$