Evaluate 49^(5/2)

$49^{\frac{5}{2}}$

Step 1

Simplify the expression.

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

${(7^{2})}^{\frac{5}{2}}$

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

$7^{2 (\frac{5}{2})}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$7^{2 (\frac{5}{2})}$

Rewrite the expression.

$7^{5}$

Step 3

Raise $7$ to the power of $5$ .

$16807$