Simplify (4x^2yz^3)^2(2xy^2z)^2

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

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

Apply the product rule to $4 x^{2} y z^{3}$ .

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

Apply the product rule to $4 x^{2} y$ .

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

Apply the product rule to $4 x^{2}$ .

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

Raise $4$ to the power of $2$ .

$16 {(x^{2})}^{2} y^{2} {(z^{3})}^{2} {(2 x y^{2} z)}^{2}$

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

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

$16 x^{2 \cdot 2} y^{2} {(z^{3})}^{2} {(2 x y^{2} z)}^{2}$

Multiply $2$ by $2$ .

$16 x^{4} y^{2} {(z^{3})}^{2} {(2 x y^{2} z)}^{2}$

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

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

$16 x^{4} y^{2} z^{3 \cdot 2} {(2 x y^{2} z)}^{2}$

Multiply $3$ by $2$ .

$16 x^{4} y^{2} z^{6} {(2 x y^{2} z)}^{2}$

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

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

$16 x^{4} y^{2} z^{6} ({(2 x y^{2})}^{2} z^{2})$

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

$16 x^{4} y^{2} z^{6} ({(2 x)}^{2} {(y^{2})}^{2} z^{2})$

Apply the product rule to $2 x$ .

$16 x^{4} y^{2} z^{6} (2^{2} x^{2} {(y^{2})}^{2} z^{2})$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$16 (x^{2} x^{4}) y^{2} z^{6} (2^{2} {(y^{2})}^{2} z^{2})$

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

$16 x^{2 + 4} y^{2} z^{6} (2^{2} {(y^{2})}^{2} z^{2})$

Add $2$ and $4$ .

$16 x^{6} y^{2} z^{6} (2^{2} {(y^{2})}^{2} z^{2})$

Multiply $z^{6}$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$16 x^{6} y^{2} (z^{2} z^{6}) (2^{2} {(y^{2})}^{2})$

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

$16 x^{6} y^{2} z^{2 + 6} (2^{2} {(y^{2})}^{2})$

Add $2$ and $6$ .

$16 x^{6} y^{2} z^{8} (2^{2} {(y^{2})}^{2})$

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

$16 x^{6} y^{2} z^{8} (4 {(y^{2})}^{2})$

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

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

$16 x^{6} y^{2} z^{8} (4 y^{2 \cdot 2})$

Multiply $2$ by $2$ .

$16 x^{6} y^{2} z^{8} (4 y^{4})$

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$16 x^{6} (y^{4} y^{2}) z^{8} \cdot 4$

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

$16 x^{6} y^{4 + 2} z^{8} \cdot 4$

Add $4$ and $2$ .

$16 x^{6} y^{6} z^{8} \cdot 4$

Multiply $4$ by $16$ .

$64 x^{6} y^{6} z^{8}$

Simplify (4x^2yz^3)^2(2xy^2z)^2

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