Evaluate (4/3)^(3(4/3))

${(\frac{4}{3})}^{3 (\frac{4}{3})}$

Step 1

Cancel the common factor of $3$ .

Cancel the common factor.

${(\frac{4}{3})}^{3 (\frac{4}{3})}$

Rewrite the expression.

${(\frac{4}{3})}^{4}$

${(\frac{4}{3})}^{4}$

Step 2

Simplify the expression.

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{4}}{3^{4}}$

Raise $4$ to the power of $4$ .

$\frac{256}{3^{4}}$

Raise $3$ to the power of $4$ .

$\frac{256}{81}$

$\frac{256}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{256}{81}$

Decimal Form:

$3.16049382 \dots$

Mixed Number Form:

$3 \frac{13}{81}$

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