Precalculus Examples

$6000 e^{\frac{\ln (\frac{11}{6})}{8} \cdot (13)}$

Rewrite $\frac{\ln (\frac{11}{6})}{8}$ as $\frac{1}{8} \ln (\frac{11}{6})$ .

$6000 e^{\frac{1}{8} \ln (\frac{11}{6}) \cdot 13}$

Simplify $\frac{1}{8} \ln (\frac{11}{6})$ by moving $\frac{1}{8}$ inside the logarithm.

$6000 e^{\ln ({(\frac{11}{6})}^{\frac{1}{8}}) \cdot 13}$

Apply the product rule to $\frac{11}{6}$ .

$6000 e^{\ln (\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}}) \cdot 13}$

Multiply $\ln (\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}}) \cdot 13$ .

Tap for more steps...

Reorder $\ln (\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}})$ and $13$ .

$6000 e^{13 \cdot \ln (\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}})}$

Simplify $13 \cdot \ln (\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}})$ by moving $13$ inside the logarithm.

$6000 e^{\ln ({(\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}})}^{13})}$

Exponentiation and log are inverse functions.

$6000 {(\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}})}^{13}$

Apply basic rules of exponents.

Tap for more steps...

Apply the product rule to $\frac{11^{\frac{1}{8}}}{6^{\frac{1}{8}}}$ .

$6000 \frac{{(11^{\frac{1}{8}})}^{13}}{{(6^{\frac{1}{8}})}^{13}}$

Multiply the exponents in ${(11^{\frac{1}{8}})}^{13}$ .

Tap for more steps...

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

$6000 \frac{11^{\frac{1}{8} \cdot 13}}{{(6^{\frac{1}{8}})}^{13}}$

Combine $\frac{1}{8}$ and $13$ .

$6000 \frac{11^{\frac{13}{8}}}{{(6^{\frac{1}{8}})}^{13}}$

Multiply the exponents in ${(6^{\frac{1}{8}})}^{13}$ .

Tap for more steps...

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

$6000 \frac{11^{\frac{13}{8}}}{6^{\frac{1}{8} \cdot 13}}$

Combine $\frac{1}{8}$ and $13$ .

$6000 \frac{11^{\frac{13}{8}}}{6^{\frac{13}{8}}}$

Combine $6000$ and $\frac{11^{\frac{13}{8}}}{6^{\frac{13}{8}}}$ .

$\frac{6000 \cdot 11^{\frac{13}{8}}}{6^{\frac{13}{8}}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{6000 \cdot 11^{\frac{13}{8}}}{6^{\frac{13}{8}}}$

Decimal Form:

$16066.40024564 \dots$