Simplify (x^3y^4z)^3(x^5y*z^3)^2

${(x^{3} \cdot y^{4} \cdot z)}^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Step 1

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

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

${(x^{3} y^{4})}^{3} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

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

${(x^{3})}^{3} {(y^{4})}^{3} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Step 2

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

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

$x^{3 \cdot 3} {(y^{4})}^{3} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Multiply $3$ by $3$ .

$x^{9} {(y^{4})}^{3} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Step 3

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

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

$x^{9} y^{4 \cdot 3} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Multiply $4$ by $3$ .

$x^{9} y^{12} z^{3} \cdot {(x^{5} \cdot y \cdot z^{3})}^{2}$

Step 4

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

Apply the product rule to $x^{5} y z^{3}$ .

$x^{9} y^{12} z^{3} \cdot ({(x^{5} y)}^{2} {(z^{3})}^{2})$

Apply the product rule to $x^{5} y$ .

$x^{9} y^{12} z^{3} \cdot ({(x^{5})}^{2} y^{2} {(z^{3})}^{2})$

Step 5

Multiply $y^{12}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$x^{9} (y^{2} y^{12}) z^{3} \cdot ({(x^{5})}^{2} {(z^{3})}^{2})$

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

$x^{9} y^{2 + 12} z^{3} \cdot ({(x^{5})}^{2} {(z^{3})}^{2})$

Add $2$ and $12$ .

$x^{9} y^{14} z^{3} \cdot ({(x^{5})}^{2} {(z^{3})}^{2})$

Step 6

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$x^{9} y^{14} z^{3} \cdot (x^{5 \cdot 2} {(z^{3})}^{2})$

Multiply $5$ by $2$ .

$x^{9} y^{14} z^{3} \cdot (x^{10} {(z^{3})}^{2})$

Step 7

Multiply $x^{9}$ by $x^{10}$ by adding the exponents.

Move $x^{10}$ .

$x^{10} x^{9} y^{14} z^{3} \cdot {(z^{3})}^{2}$

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

$x^{10 + 9} y^{14} z^{3} \cdot {(z^{3})}^{2}$

Add $10$ and $9$ .

$x^{19} y^{14} z^{3} \cdot {(z^{3})}^{2}$

Step 8

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

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

$x^{19} y^{14} z^{3} \cdot z^{3 \cdot 2}$

Multiply $3$ by $2$ .

$x^{19} y^{14} z^{3} \cdot z^{6}$

Step 9

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

Move $z^{6}$ .

$x^{19} y^{14} (z^{6} z^{3})$

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

$x^{19} y^{14} z^{6 + 3}$

Add $6$ and $3$ .

$x^{19} y^{14} z^{9}$

Simplify (x^3*y^4*z)^3*(x^5*y*z^3)^2

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Simplify (x^3y^4z)^3(x^5y*z^3)^2