Precalculus Examples

$a (30) = 3900 {(\frac{1}{2})}^{\frac{30}{14}}$

Step 1

Simplify.

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Step 1.1

Cancel the common factor of $30$ and $14$ .

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Step 1.1.1

Factor $2$ out of $30$ .

$a (30) = 3900 {(\frac{1}{2})}^{\frac{2 (15)}{14}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $14$ .

$a (30) = 3900 {(\frac{1}{2})}^{\frac{2 \cdot 15}{2 \cdot 7}}$

Step 1.1.2.2

Cancel the common factor.

$a (30) = 3900 {(\frac{1}{2})}^{\frac{2 \cdot 15}{2 \cdot 7}}$

Step 1.1.2.3

Rewrite the expression.

$a (30) = 3900 {(\frac{1}{2})}^{\frac{15}{7}}$

Step 1.2

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

$a (30) = 3900 \frac{1^{\frac{15}{7}}}{2^{\frac{15}{7}}}$

Step 1.3

One to any power is one.

$a (30) = 3900 \frac{1}{2^{\frac{15}{7}}}$

Step 1.4

Combine $3900$ and $\frac{1}{2^{\frac{15}{7}}}$ .

$a (30) = \frac{3900}{2^{\frac{15}{7}}}$

Step 2

Divide each term in $a (30) = \frac{3900}{2^{\frac{15}{7}}}$ by $30$ and simplify.

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Step 2.1

Divide each term in $a (30) = \frac{3900}{2^{\frac{15}{7}}}$ by $30$ .

$\frac{a (30)}{30} = \frac{\frac{3900}{2^{\frac{15}{7}}}}{30}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $30$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a \cdot 30}{30} = \frac{\frac{3900}{2^{\frac{15}{7}}}}{30}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{\frac{3900}{2^{\frac{15}{7}}}}{30}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{3900}{2^{\frac{15}{7}}} \cdot \frac{1}{30}$

Step 2.3.2

Combine.

$a = \frac{3900 \cdot 1}{2^{\frac{15}{7}} \cdot 30}$

Step 2.3.3

Factor $30$ out of $3900 \cdot 1$ .

$a = \frac{30 (130 \cdot 1)}{2^{\frac{15}{7}} \cdot 30}$

Step 2.3.4

Cancel the common factors.

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Step 2.3.4.1

Factor $30$ out of $2^{\frac{15}{7}} \cdot 30$ .

$a = \frac{30 (130 \cdot 1)}{30 \cdot 2^{\frac{15}{7}}}$

Step 2.3.4.2

Cancel the common factor.

$a = \frac{30 (130 \cdot 1)}{30 \cdot 2^{\frac{15}{7}}}$

Step 2.3.4.3

Rewrite the expression.

$a = \frac{130 \cdot 1}{2^{\frac{15}{7}}}$

Step 2.3.5

Multiply $130$ by $1$ .

$a = \frac{130}{2^{\frac{15}{7}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{130}{2^{\frac{15}{7}}}$

Decimal Form:

$a = 29.43601908 \dots$