Simplify (8x^4y^2)/(3z^3)*(9xy^2z^6)/(4y^4)

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

Step 1

Combine.

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

Step 2

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

Move $x$ .

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

Multiply $x$ by $x^{4}$ .

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

$\frac{8 (x^{1} x^{4}) y^{2} (9 y^{2} z^{6})}{3 z^{3} (4 y^{4})}$

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

$\frac{8 x^{1 + 4} y^{2} (9 y^{2} z^{6})}{3 z^{3} (4 y^{4})}$

Add $1$ and $4$ .

$\frac{8 x^{5} y^{2} (9 y^{2} z^{6})}{3 z^{3} (4 y^{4})}$

Step 3

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

Move $y^{2}$ .

$\frac{8 x^{5} (y^{2} y^{2}) (9 z^{6})}{3 z^{3} (4 y^{4})}$

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

$\frac{8 x^{5} y^{2 + 2} (9 z^{6})}{3 z^{3} (4 y^{4})}$

Add $2$ and $2$ .

$\frac{8 x^{5} y^{4} (9 z^{6})}{3 z^{3} (4 y^{4})}$

Step 4

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 x^{5} y^{4} (9 z^{6})$ .

$\frac{4 (2 x^{5} y^{4} (9 z^{6}))}{3 z^{3} (4 y^{4})}$

Cancel the common factors.

Factor $4$ out of $3 z^{3} (4 y^{4})$ .

$\frac{4 (2 x^{5} y^{4} (9 z^{6}))}{4 (3 z^{3} (y^{4}))}$

Cancel the common factor.

$\frac{4 (2 x^{5} y^{4} (9 z^{6}))}{4 (3 z^{3} (y^{4}))}$

Rewrite the expression.

$\frac{2 x^{5} y^{4} (9 z^{6})}{3 z^{3} (y^{4})}$

Step 5

Cancel the common factor of $y^{4}$ .

Cancel the common factor.

$\frac{2 x^{5} y^{4} (9 z^{6})}{3 z^{3} y^{4}}$

Rewrite the expression.

$\frac{2 x^{5} (9 z^{6})}{3 z^{3}}$

Step 6

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $2 x^{5} (9 z^{6})$ .

$\frac{3 (2 x^{5} (3 z^{6}))}{3 z^{3}}$

Cancel the common factors.

Factor $3$ out of $3 z^{3}$ .

$\frac{3 (2 x^{5} (3 z^{6}))}{3 (z^{3})}$

Cancel the common factor.

$\frac{3 (2 x^{5} (3 z^{6}))}{3 z^{3}}$

Rewrite the expression.

$\frac{2 x^{5} (3 z^{6})}{z^{3}}$

Step 7

Cancel the common factor of $z^{6}$ and $z^{3}$ .

Factor $z^{3}$ out of $2 x^{5} (3 z^{6})$ .

$\frac{z^{3} (2 x^{5} (3 z^{3}))}{z^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{z^{3} (2 x^{5} (3 z^{3}))}{z^{3} \cdot 1}$

Cancel the common factor.

$\frac{z^{3} (2 x^{5} (3 z^{3}))}{z^{3} \cdot 1}$

Rewrite the expression.

$\frac{2 x^{5} (3 z^{3})}{1}$

Divide $2 x^{5} (3 z^{3})$ by $1$ .

$2 x^{5} (3 z^{3})$

Step 8

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x^{5} z^{3}$

Multiply $2$ by $3$ .

$6 x^{5} z^{3}$

Simplify (8x^4y^2)/(3z^3)*(9xy^2z^6)/(4y^4)

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