Simplify (m^(4/7)n^3)^7(m^4)^3

${(m^{\frac{4}{7}} n^{3})}^{7} {(m^{4})}^{3}$

Step 1

Apply the product rule to $m^{\frac{4}{7}} n^{3}$ .

${(m^{\frac{4}{7}})}^{7} {(n^{3})}^{7} {(m^{4})}^{3}$

Step 2

Multiply the exponents in ${(m^{\frac{4}{7}})}^{7}$ .

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

$m^{\frac{4}{7} \cdot 7} {(n^{3})}^{7} {(m^{4})}^{3}$

Cancel the common factor of $7$ .

Cancel the common factor.

$m^{\frac{4}{7} \cdot 7} {(n^{3})}^{7} {(m^{4})}^{3}$

Rewrite the expression.

$m^{4} {(n^{3})}^{7} {(m^{4})}^{3}$

Step 3

Multiply the exponents in ${(n^{3})}^{7}$ .

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

$m^{4} n^{3 \cdot 7} {(m^{4})}^{3}$

Multiply $3$ by $7$ .

$m^{4} n^{21} {(m^{4})}^{3}$

Step 4

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

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

$m^{4} n^{21} m^{4 \cdot 3}$

Multiply $4$ by $3$ .

$m^{4} n^{21} m^{12}$

Step 5

Multiply $m^{4}$ by $m^{12}$ by adding the exponents.

Move $m^{12}$ .

$m^{12} m^{4} n^{21}$

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

$m^{12 + 4} n^{21}$

Add $12$ and $4$ .

$m^{16} n^{21}$