Evaluate (49^3)^(1/6)

${(49^{3})}^{\frac{1}{6}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(49^{3})}^{\frac{1}{6}}$ .

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

$49^{3 (\frac{1}{6})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$49^{3 \frac{1}{3 (2)}}$

Cancel the common factor.

$49^{3 \frac{1}{3 \cdot 2}}$

Rewrite the expression.

$49^{\frac{1}{2}}$

Rewrite $49$ as $7^{2}$ .

${(7^{2})}^{\frac{1}{2}}$

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

$7^{2 (\frac{1}{2})}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$7^{2 (\frac{1}{2})}$

Rewrite the expression.

$7^{1}$

Step 3

Evaluate the exponent.

$7$