Evaluate (3^21*3^-7)/((3^2)^5)

$\frac{3^{21} \cdot 3^{- 7}}{{(3^{2})}^{5}}$

Step 1

Multiply $3^{21}$ by $3^{- 7}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3^{21 - 7}}{{(3^{2})}^{5}}$

Subtract $7$ from $21$ .

$\frac{3^{14}}{{(3^{2})}^{5}}$

Step 2

Raise $3$ to the power of $14$ .

$\frac{4782969}{{(3^{2})}^{5}}$

Step 3

Simplify the denominator.

Multiply the exponents in ${(3^{2})}^{5}$ .

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

$\frac{4782969}{3^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{4782969}{3^{10}}$

Raise $3$ to the power of $10$ .

$\frac{4782969}{59049}$

Step 4

Divide $4782969$ by $59049$ .

$81$