Simplify (9^7)^(3/14)

${(9^{7})}^{\frac{3}{14}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(9^{7})}^{\frac{3}{14}}$ .

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

$9^{7 (\frac{3}{14})}$

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$9^{7 \frac{3}{7 (2)}}$

Cancel the common factor.

$9^{7 \frac{3}{7 \cdot 2}}$

Rewrite the expression.

$9^{\frac{3}{2}}$

Rewrite $9$ as $3^{2}$ .

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{3}$

Step 3

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

$27$