Simplify (18xy^3z^2)(x^3yz^5)^3(z^6)^2

$(18 x y^{3} z^{2}) {(x^{3} y z^{5})}^{3} {(z^{6})}^{2}$

Step 1

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

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

$18 x y^{3} z^{2} ({(x^{3} y)}^{3} {(z^{5})}^{3}) {(z^{6})}^{2}$

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

$18 x y^{3} z^{2} ({(x^{3})}^{3} y^{3} {(z^{5})}^{3}) {(z^{6})}^{2}$

Step 2

Multiply $y^{3}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$18 x (y^{3} y^{3}) z^{2} ({(x^{3})}^{3} {(z^{5})}^{3}) {(z^{6})}^{2}$

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

$18 x y^{3 + 3} z^{2} ({(x^{3})}^{3} {(z^{5})}^{3}) {(z^{6})}^{2}$

Add $3$ and $3$ .

$18 x y^{6} z^{2} ({(x^{3})}^{3} {(z^{5})}^{3}) {(z^{6})}^{2}$

Step 3

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

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

$18 x y^{6} z^{2} (x^{3 \cdot 3} {(z^{5})}^{3}) {(z^{6})}^{2}$

Multiply $3$ by $3$ .

$18 x y^{6} z^{2} (x^{9} {(z^{5})}^{3}) {(z^{6})}^{2}$

Step 4

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

Move $x^{9}$ .

$18 (x^{9} x) y^{6} z^{2} {(z^{5})}^{3} {(z^{6})}^{2}$

Multiply $x^{9}$ by $x$ .

Raise $x$ to the power of $1$ .

$18 (x^{9} x^{1}) y^{6} z^{2} {(z^{5})}^{3} {(z^{6})}^{2}$

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

$18 x^{9 + 1} y^{6} z^{2} {(z^{5})}^{3} {(z^{6})}^{2}$

Add $9$ and $1$ .

$18 x^{10} y^{6} z^{2} {(z^{5})}^{3} {(z^{6})}^{2}$

Step 5

Multiply the exponents in ${(z^{5})}^{3}$ .

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

$18 x^{10} y^{6} z^{2} z^{5 \cdot 3} {(z^{6})}^{2}$

Multiply $5$ by $3$ .

$18 x^{10} y^{6} z^{2} z^{15} {(z^{6})}^{2}$

Step 6

Multiply $z^{2}$ by $z^{15}$ by adding the exponents.

Move $z^{15}$ .

$18 x^{10} y^{6} (z^{15} z^{2}) {(z^{6})}^{2}$

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

$18 x^{10} y^{6} z^{15 + 2} {(z^{6})}^{2}$

Add $15$ and $2$ .

$18 x^{10} y^{6} z^{17} {(z^{6})}^{2}$

Step 7

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

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

$18 x^{10} y^{6} z^{17} z^{6 \cdot 2}$

Multiply $6$ by $2$ .

$18 x^{10} y^{6} z^{17} z^{12}$

Step 8

Multiply $z^{17}$ by $z^{12}$ by adding the exponents.

Move $z^{12}$ .

$18 x^{10} y^{6} (z^{12} z^{17})$

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

$18 x^{10} y^{6} z^{12 + 17}$

Add $12$ and $17$ .

$18 x^{10} y^{6} z^{29}$

Simplify (18xy^3z^2)(x^3yz^5)^3(z^6)^2

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