Precalculus Examples

${(e^{\frac{3}{2}})}^{\ln (4)}$

Step 1

Multiply the exponents in ${(e^{\frac{3}{2}})}^{\ln (4)}$ .

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Step 1.1

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

$e^{\frac{3}{2} \ln (4)}$

Step 1.2

Simplify $\frac{3}{2} \ln (4)$ by moving $\frac{3}{2}$ inside the logarithm.

$e^{\ln (4^{\frac{3}{2}})}$

Step 1.3

Rewrite $4$ as $2^{2}$ .

$e^{\ln ({(2^{2})}^{\frac{3}{2}})}$

Step 1.4

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

$e^{\ln (2^{2 (\frac{3}{2})})}$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Cancel the common factor.

$e^{\ln (2^{2 (\frac{3}{2})})}$

Step 1.5.2

Rewrite the expression.

$e^{\ln (2^{3})}$

Step 1.6

Raise $2$ to the power of $3$ .

$e^{\ln (8)}$

Step 2

Exponentiation and log are inverse functions.

$8$