Simplify (m^4n)^3*(m^5n^3)^2

${(m^{4} n)}^{3} \cdot {(m^{5} n^{3})}^{2}$

Apply the product rule to $m^{4} n$ .

${(m^{4})}^{3} n^{3} \cdot {(m^{5} n^{3})}^{2}$

Multiply the exponents in ${(m^{4})}^{3}$ .

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

$m^{4 \cdot 3} n^{3} \cdot {(m^{5} n^{3})}^{2}$

Multiply $4$ by $3$ .

$m^{12} n^{3} \cdot {(m^{5} n^{3})}^{2}$

Apply the product rule to $m^{5} n^{3}$ .

$m^{12} n^{3} \cdot ({(m^{5})}^{2} {(n^{3})}^{2})$

Multiply the exponents in ${(m^{5})}^{2}$ .

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

$m^{12} n^{3} \cdot (m^{5 \cdot 2} {(n^{3})}^{2})$

Multiply $5$ by $2$ .

$m^{12} n^{3} \cdot (m^{10} {(n^{3})}^{2})$

Multiply $m^{12}$ by $m^{10}$ by adding the exponents.

Move $m^{10}$ .

$m^{10} m^{12} n^{3} \cdot {(n^{3})}^{2}$

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

$m^{10 + 12} n^{3} \cdot {(n^{3})}^{2}$

Add $10$ and $12$ .

$m^{22} n^{3} \cdot {(n^{3})}^{2}$

Multiply the exponents in ${(n^{3})}^{2}$ .

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

$m^{22} n^{3} \cdot n^{3 \cdot 2}$

Multiply $3$ by $2$ .

$m^{22} n^{3} \cdot n^{6}$

Multiply $n^{3}$ by $n^{6}$ by adding the exponents.

Move $n^{6}$ .

$m^{22} (n^{6} n^{3})$

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

$m^{22} n^{6 + 3}$

Add $6$ and $3$ .

$m^{22} n^{9}$