Simplify 2a^(1/m)*4^ma^(5+m)

$2 a^{\frac{1}{m}} \cdot 4^{m} a^{5 + m}$

Multiply $a^{\frac{1}{m}}$ by $a^{5 + m}$ by adding the exponents.

Move $a^{5 + m}$ .

$2 (a^{5 + m} a^{\frac{1}{m}}) \cdot 4^{m}$

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

$2 a^{5 + m + \frac{1}{m}} \cdot 4^{m}$

Multiply $2 a^{5 + m + \frac{1}{m}} \cdot 4^{m}$ .

Rewrite $4$ as $2^{2}$ .

${(2^{2})}^{m} \cdot 2 a^{5 + m + \frac{1}{m}}$

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

$2^{2 m} \cdot 2 a^{5 + m + \frac{1}{m}}$

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

$2^{2 m + 1} a^{5 + m + \frac{1}{m}}$