Simplify (-7ab^4c)^3((2a^2c)^2)^3

${(- 7 a b^{4} c)}^{3} {({(2 a^{2} c)}^{2})}^{3}$

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

Apply the product rule to $- 7 a b^{4} c$ .

${(- 7 a b^{4})}^{3} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

Apply the product rule to $- 7 a b^{4}$ .

${(- 7 a)}^{3} {(b^{4})}^{3} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

Apply the product rule to $- 7 a$ .

${(- 7)}^{3} a^{3} {(b^{4})}^{3} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

Raise $- 7$ to the power of $3$ .

$- 343 a^{3} {(b^{4})}^{3} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

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

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

$- 343 a^{3} b^{4 \cdot 3} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

Multiply $4$ by $3$ .

$- 343 a^{3} b^{12} c^{3} {({(2 a^{2} c)}^{2})}^{3}$

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

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

$- 343 a^{3} b^{12} c^{3} {(2 a^{2} c)}^{2 \cdot 3}$

Multiply $2$ by $3$ .

$- 343 a^{3} b^{12} c^{3} {(2 a^{2} c)}^{6}$

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

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

$- 343 a^{3} b^{12} c^{3} ({(2 a^{2})}^{6} c^{6})$

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

$- 343 a^{3} b^{12} c^{3} (2^{6} {(a^{2})}^{6} c^{6})$

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

Move $c^{6}$ .

$- 343 a^{3} b^{12} (c^{6} c^{3}) (2^{6} {(a^{2})}^{6})$

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

$- 343 a^{3} b^{12} c^{6 + 3} (2^{6} {(a^{2})}^{6})$

Add $6$ and $3$ .

$- 343 a^{3} b^{12} c^{9} (2^{6} {(a^{2})}^{6})$

Raise $2$ to the power of $6$ .

$- 343 a^{3} b^{12} c^{9} (64 {(a^{2})}^{6})$

Multiply the exponents in ${(a^{2})}^{6}$ .

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

$- 343 a^{3} b^{12} c^{9} (64 a^{2 \cdot 6})$

Multiply $2$ by $6$ .

$- 343 a^{3} b^{12} c^{9} (64 a^{12})$

Multiply $a^{3}$ by $a^{12}$ by adding the exponents.

Move $a^{12}$ .

$- 343 (a^{12} a^{3}) b^{12} c^{9} \cdot 64$

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

$- 343 a^{12 + 3} b^{12} c^{9} \cdot 64$

Add $12$ and $3$ .

$- 343 a^{15} b^{12} c^{9} \cdot 64$

Multiply $64$ by $- 343$ .

$- 21952 a^{15} b^{12} c^{9}$

Simplify (-7ab^4c)^3((2a^2c)^2)^3

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