Simplify (5a^2b^3c^4)^4(6a^3b^4c^2)

${(5 a^{2} b^{3} c^{4})}^{4} (6 a^{3} b^{4} c^{2})$

Rewrite using the commutative property of multiplication.

$6 {(5 a^{2} b^{3} c^{4})}^{4} a^{3} b^{4} c^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $5 a^{2} b^{3} c^{4}$ .

$6 ({(5 a^{2} b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Apply the product rule to $5 a^{2} b^{3}$ .

$6 ({(5 a^{2})}^{4} {(b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Apply the product rule to $5 a^{2}$ .

$6 (5^{4} {(a^{2})}^{4} {(b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Raise $5$ to the power of $4$ .

$6 (625 {(a^{2})}^{4} {(b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Multiply the exponents in ${(a^{2})}^{4}$ .

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

$6 (625 a^{2 \cdot 4} {(b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Multiply $2$ by $4$ .

$6 (625 a^{8} {(b^{3})}^{4} {(c^{4})}^{4}) a^{3} b^{4} c^{2}$

Multiply $a^{8}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$6 (625 (a^{3} a^{8}) {(b^{3})}^{4} {(c^{4})}^{4}) b^{4} c^{2}$

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

$6 (625 a^{3 + 8} {(b^{3})}^{4} {(c^{4})}^{4}) b^{4} c^{2}$

Add $3$ and $8$ .

$6 (625 a^{11} {(b^{3})}^{4} {(c^{4})}^{4}) b^{4} c^{2}$

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

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

$6 (625 a^{11} b^{3 \cdot 4} {(c^{4})}^{4}) b^{4} c^{2}$

Multiply $3$ by $4$ .

$6 (625 a^{11} b^{12} {(c^{4})}^{4}) b^{4} c^{2}$

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

Move $b^{4}$ .

$6 (625 a^{11} (b^{4} b^{12}) {(c^{4})}^{4}) c^{2}$

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

$6 (625 a^{11} b^{4 + 12} {(c^{4})}^{4}) c^{2}$

Add $4$ and $12$ .

$6 (625 a^{11} b^{16} {(c^{4})}^{4}) c^{2}$

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

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

$6 (625 a^{11} b^{16} c^{4 \cdot 4}) c^{2}$

Multiply $4$ by $4$ .

$6 (625 a^{11} b^{16} c^{16}) c^{2}$

Multiply $c^{16}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

$6 (625 a^{11} b^{16} (c^{2} c^{16}))$

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

$6 (625 a^{11} b^{16} c^{2 + 16})$

Add $2$ and $16$ .

$6 (625 a^{11} b^{16} c^{18})$

Multiply $625$ by $6$ .

$3750 a^{11} b^{16} c^{18}$

Simplify (5a^2b^3c^4)^4(6a^3b^4c^2)

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