Simplify (4r^(2/5)5s^(2/7))(5s^(5/7)4r^(3/5))

$(4 r^{\frac{2}{5}} \cdot 5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot 4 r^{\frac{3}{5}})$

Multiply $r^{\frac{2}{5}}$ by $r^{\frac{3}{5}}$ by adding the exponents.

Move $r^{\frac{3}{5}}$ .

$4 (r^{\frac{3}{5}} r^{\frac{2}{5}}) \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

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

$4 r^{\frac{3}{5} + \frac{2}{5}} \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

Combine the numerators over the common denominator.

$4 r^{\frac{3 + 2}{5}} \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

Add $3$ and $2$ .

$4 r^{\frac{5}{5}} \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

Divide $5$ by $5$ .

$4 r^{1} \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

Simplify $4 r^{1} \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$ .

$4 r \cdot (5 s^{\frac{2}{7}}) (5 s^{\frac{5}{7}} \cdot (4))$

Multiply $s^{\frac{2}{7}}$ by $s^{\frac{5}{7}}$ by adding the exponents.

Move $s^{\frac{5}{7}}$ .

$4 r \cdot (5 (s^{\frac{5}{7}} s^{\frac{2}{7}})) (5 \cdot (4))$

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

$4 r \cdot (5 s^{\frac{5}{7} + \frac{2}{7}}) (5 \cdot (4))$

Combine the numerators over the common denominator.

$4 r \cdot (5 s^{\frac{5 + 2}{7}}) (5 \cdot (4))$

Add $5$ and $2$ .

$4 r \cdot (5 s^{\frac{7}{7}}) (5 \cdot (4))$

Divide $7$ by $7$ .

$4 r \cdot (5 s^{1}) (5 \cdot (4))$

Simplify $4 r \cdot (5 s^{1}) (5 \cdot (4))$ .

$4 r \cdot (5 s) (5 \cdot (4))$

Rewrite using the commutative property of multiplication.

$4 \cdot 5 r s (5 \cdot (4))$

Multiply $4$ by $5$ .

$20 r s (5 \cdot (4))$

Multiply $5$ by $4$ .

$20 r s \cdot 20$

Multiply $20$ by $20$ .

$400 r s$

Simplify (4r^(2/5)*5s^(2/7))(5s^(5/7)*4r^(3/5))