Simplify 7^(1/5)*49^(7/5)

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$

Multiply $7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ .

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

$7^{\frac{1}{5}} \cdot {(7^{2})}^{\frac{7}{5}}$

Multiply the exponents in ${(7^{2})}^{\frac{7}{5}}$ .

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

$7^{\frac{1}{5}} \cdot 7^{2 (\frac{7}{5})}$

Multiply $2 (\frac{7}{5})$ .

Combine $2$ and $\frac{7}{5}$ .

$7^{\frac{1}{5}} \cdot 7^{\frac{2 \cdot 7}{5}}$

Multiply $2$ by $7$ .

$7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}$

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

$7^{\frac{1}{5} + \frac{14}{5}}$

Combine the numerators over the common denominator.

$7^{\frac{1 + 14}{5}}$

Add $1$ and $14$ .

$7^{\frac{15}{5}}$

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15$ .

$7^{\frac{5 \cdot 3}{5}}$

Cancel the common factors.

Factor $5$ out of $5$ .

$7^{\frac{5 \cdot 3}{5 (1)}}$

Cancel the common factor.

$7^{\frac{5 \cdot 3}{5 \cdot 1}}$

Rewrite the expression.

$7^{\frac{3}{1}}$

Divide $3$ by $1$ .

$7^{3}$

Raise $7$ to the power of $3$ .

$343$