Precalculus Examples

$72 + 253 e^{\frac{1}{10} \cdot \ln (\frac{128}{253}) \cdot 30}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $\frac{1}{10} \ln (\frac{128}{253})$ by moving $\frac{1}{10}$ inside the logarithm.

$72 + 253 e^{\ln ({(\frac{128}{253})}^{\frac{1}{10}}) \cdot 30}$

Step 1.2

Apply the product rule to $\frac{128}{253}$ .

$72 + 253 e^{\ln (\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}}) \cdot 30}$

Step 1.3

Multiply $\ln (\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}}) \cdot 30$ .

Tap for more steps...

Step 1.3.1

Reorder $\ln (\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}})$ and $30$ .

$72 + 253 e^{30 \cdot \ln (\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}})}$

Step 1.3.2

Simplify $30 \cdot \ln (\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}})$ by moving $30$ inside the logarithm.

$72 + 253 e^{\ln ({(\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}})}^{30})}$

Step 1.4

Exponentiation and log are inverse functions.

$72 + 253 {(\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}})}^{30}$

Step 1.5

Apply the product rule to $\frac{128^{\frac{1}{10}}}{253^{\frac{1}{10}}}$ .

$72 + 253 \frac{{(128^{\frac{1}{10}})}^{30}}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.6

Simplify the numerator.

Tap for more steps...

Step 1.6.1

Multiply the exponents in ${(128^{\frac{1}{10}})}^{30}$ .

Tap for more steps...

Step 1.6.1.1

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

$72 + 253 \frac{128^{\frac{1}{10} \cdot 30}}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.6.1.2

Cancel the common factor of $10$ .

Tap for more steps...

Step 1.6.1.2.1

Factor $10$ out of $30$ .

$72 + 253 \frac{128^{\frac{1}{10} \cdot (10 (3))}}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.6.1.2.2

Cancel the common factor.

$72 + 253 \frac{128^{\frac{1}{10} \cdot (10 \cdot 3)}}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.6.1.2.3

Rewrite the expression.

$72 + 253 \frac{128^{3}}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.6.2

Raise $128$ to the power of $3$ .

$72 + 253 \frac{2097152}{{(253^{\frac{1}{10}})}^{30}}$

Step 1.7

Simplify the denominator.

Tap for more steps...

Step 1.7.1

Multiply the exponents in ${(253^{\frac{1}{10}})}^{30}$ .

Tap for more steps...

Step 1.7.1.1

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

$72 + 253 \frac{2097152}{253^{\frac{1}{10} \cdot 30}}$

Step 1.7.1.2

Cancel the common factor of $10$ .

Tap for more steps...

Step 1.7.1.2.1

Factor $10$ out of $30$ .

$72 + 253 \frac{2097152}{253^{\frac{1}{10} \cdot (10 (3))}}$

Step 1.7.1.2.2

Cancel the common factor.

$72 + 253 \frac{2097152}{253^{\frac{1}{10} \cdot (10 \cdot 3)}}$

Step 1.7.1.2.3

Rewrite the expression.

$72 + 253 \frac{2097152}{253^{3}}$

Step 1.7.2

Raise $253$ to the power of $3$ .

$72 + 253 (\frac{2097152}{16194277})$

Step 1.8

Cancel the common factor of $253$ .

Tap for more steps...

Step 1.8.1

Factor $253$ out of $16194277$ .

$72 + 253 \frac{2097152}{253 (64009)}$

Step 1.8.2

Cancel the common factor.

$72 + 253 \frac{2097152}{253 \cdot 64009}$

Step 1.8.3

Rewrite the expression.

$72 + \frac{2097152}{64009}$

Step 2

To write $72$ as a fraction with a common denominator, multiply by $\frac{64009}{64009}$ .

$72 \cdot \frac{64009}{64009} + \frac{2097152}{64009}$

Step 3

Combine $72$ and $\frac{64009}{64009}$ .

$\frac{72 \cdot 64009}{64009} + \frac{2097152}{64009}$

Step 4

Combine the numerators over the common denominator.

$\frac{72 \cdot 64009 + 2097152}{64009}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $72$ by $64009$ .

$\frac{4608648 + 2097152}{64009}$

Step 5.2

Add $4608648$ and $2097152$ .

$\frac{6705800}{64009}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{6705800}{64009}$

Decimal Form:

$104.76339264 \dots$

Mixed Number Form:

$104 \frac{48864}{64009}$