Precalculus Examples

$50 {(e)}^{(\frac{1}{1690} \cdot \ln (\frac{1}{2})) (970)}$

Step 1

Simplify $\frac{1}{1690} \ln (\frac{1}{2})$ by moving $\frac{1}{1690}$ inside the logarithm.

$50 e^{\ln ({(\frac{1}{2})}^{\frac{1}{1690}}) \cdot 970}$

Step 2

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

$50 e^{\ln (\frac{1^{\frac{1}{1690}}}{2^{\frac{1}{1690}}}) \cdot 970}$

Step 3

One to any power is one.

$50 e^{\ln (\frac{1}{2^{\frac{1}{1690}}}) \cdot 970}$

Step 4

Multiply $\ln (\frac{1}{2^{\frac{1}{1690}}}) \cdot 970$ .

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Step 4.1

Reorder $\ln (\frac{1}{2^{\frac{1}{1690}}})$ and $970$ .

$50 e^{970 \cdot \ln (\frac{1}{2^{\frac{1}{1690}}})}$

Step 4.2

Simplify $970 \cdot \ln (\frac{1}{2^{\frac{1}{1690}}})$ by moving $970$ inside the logarithm.

$50 e^{\ln ({(\frac{1}{2^{\frac{1}{1690}}})}^{970})}$

Step 5

Exponentiation and log are inverse functions.

$50 {(\frac{1}{2^{\frac{1}{1690}}})}^{970}$

Step 6

Simplify the expression.

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Step 6.1

Apply the product rule to $\frac{1}{2^{\frac{1}{1690}}}$ .

$50 \frac{1^{970}}{{(2^{\frac{1}{1690}})}^{970}}$

Step 6.2

One to any power is one.

$50 \frac{1}{{(2^{\frac{1}{1690}})}^{970}}$

Step 6.3

Multiply the exponents in ${(2^{\frac{1}{1690}})}^{970}$ .

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Step 6.3.1

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

$50 \frac{1}{2^{\frac{1}{1690} \cdot 970}}$

Step 6.3.2

Cancel the common factor of $10$ .

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Step 6.3.2.1

Factor $10$ out of $1690$ .

$50 \frac{1}{2^{\frac{1}{10 (169)} \cdot 970}}$

Step 6.3.2.2

Factor $10$ out of $970$ .

$50 \frac{1}{2^{\frac{1}{10 \cdot 169} \cdot (10 \cdot 97)}}$

Step 6.3.2.3

Cancel the common factor.

$50 \frac{1}{2^{\frac{1}{10 \cdot 169} \cdot (10 \cdot 97)}}$

Step 6.3.2.4

Rewrite the expression.

$50 \frac{1}{2^{\frac{1}{169} \cdot 97}}$

Step 6.3.3

Combine $\frac{1}{169}$ and $97$ .

$50 \frac{1}{2^{\frac{97}{169}}}$

Step 7

Combine $50$ and $\frac{1}{2^{\frac{97}{169}}}$ .

$\frac{50}{2^{\frac{97}{169}}}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{50}{2^{\frac{97}{169}}}$

Decimal Form:

$33.58841220 \dots$