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Evaluate ((32)^6)/((71)^4)

$\frac{{(3 \cdot 2)}^{6}}{{(7 \cdot 1)}^{4}}$

Step 1

Simplify the numerator.

Apply the product rule to $3 \cdot 2$ .

$\frac{3^{6} \cdot 2^{6}}{{(7 \cdot 1)}^{4}}$

Raise $3$ to the power of $6$ .

$\frac{729 \cdot 2^{6}}{{(7 \cdot 1)}^{4}}$

Raise $2$ to the power of $6$ .

$\frac{729 \cdot 64}{{(7 \cdot 1)}^{4}}$

$\frac{729 \cdot 64}{{(7 \cdot 1)}^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $7 \cdot 1$ .

$\frac{729 \cdot 64}{7^{4} \cdot 1^{4}}$

Raise $7$ to the power of $4$ .

$\frac{729 \cdot 64}{2401 \cdot 1^{4}}$

One to any power is one.

$\frac{729 \cdot 64}{2401 \cdot 1}$

$\frac{729 \cdot 64}{2401 \cdot 1}$

Step 3

Multiply.

Multiply $729$ by $64$ .

$\frac{46656}{2401 \cdot 1}$

Multiply $2401$ by $1$ .

$\frac{46656}{2401}$

$\frac{46656}{2401}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{46656}{2401}$

Decimal Form:

$19.43190337 \dots$

Mixed Number Form:

$19 \frac{1037}{2401}$

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