Evaluate (2x^3y^2z^2)^3(x^2z)^4

${(2 x^{3} y^{2} z^{2})}^{3} {(x^{2} z)}^{4}$

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

Apply the product rule to $2 x^{3} y^{2} z^{2}$ .

${(2 x^{3} y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

Apply the product rule to $2 x^{3} y^{2}$ .

${(2 x^{3})}^{3} {(y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

Apply the product rule to $2 x^{3}$ .

$2^{3} {(x^{3})}^{3} {(y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

Raise $2$ to the power of $3$ .

$8 {(x^{3})}^{3} {(y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

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

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

$8 x^{3 \cdot 3} {(y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

Multiply $3$ by $3$ .

$8 x^{9} {(y^{2})}^{3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

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

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

$8 x^{9} y^{2 \cdot 3} {(z^{2})}^{3} {(x^{2} z)}^{4}$

Multiply $2$ by $3$ .

$8 x^{9} y^{6} {(z^{2})}^{3} {(x^{2} z)}^{4}$

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

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

$8 x^{9} y^{6} z^{2 \cdot 3} {(x^{2} z)}^{4}$

Multiply $2$ by $3$ .

$8 x^{9} y^{6} z^{6} {(x^{2} z)}^{4}$

Apply the product rule to $x^{2} z$ .

$8 x^{9} y^{6} z^{6} ({(x^{2})}^{4} z^{4})$

Multiply $z^{6}$ by $z^{4}$ by adding the exponents.

Move $z^{4}$ .

$8 x^{9} y^{6} (z^{4} z^{6}) {(x^{2})}^{4}$

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

$8 x^{9} y^{6} z^{4 + 6} {(x^{2})}^{4}$

Add $4$ and $6$ .

$8 x^{9} y^{6} z^{10} {(x^{2})}^{4}$

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

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

$8 x^{9} y^{6} z^{10} x^{2 \cdot 4}$

Multiply $2$ by $4$ .

$8 x^{9} y^{6} z^{10} x^{8}$

Multiply $x^{9}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$8 (x^{8} x^{9}) y^{6} z^{10}$

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

$8 x^{8 + 9} y^{6} z^{10}$

Add $8$ and $9$ .

$8 x^{17} y^{6} z^{10}$

Evaluate (2x^3y^2z^2)^3(x^2z)^4

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