Simplify ((32)^5)÷(3^22^3)

${(3 \cdot 2)}^{5} \div (3^{2} \cdot 2^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{{(3 \cdot 2)}^{5}}{3^{2} \cdot 2^{3}}$

Step 2

Simplify the numerator.

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

$\frac{3^{5} \cdot 2^{5}}{3^{2} \cdot 2^{3}}$

Raise $3$ to the power of $5$ .

$\frac{243 \cdot 2^{5}}{3^{2} \cdot 2^{3}}$

Raise $2$ to the power of $5$ .

$\frac{243 \cdot 32}{3^{2} \cdot 2^{3}}$

$\frac{243 \cdot 32}{3^{2} \cdot 2^{3}}$

Step 3

Simplify the denominator.

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

$\frac{243 \cdot 32}{9 \cdot 2^{3}}$

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

$\frac{243 \cdot 32}{9 \cdot 8}$

$\frac{243 \cdot 32}{9 \cdot 8}$

Step 4

Simplify the expression.

Multiply $243$ by $32$ .

$\frac{7776}{9 \cdot 8}$

Multiply $9$ by $8$ .

$\frac{7776}{72}$

Divide $7776$ by $72$ .

$108$

$108$

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