Simplify (4x^2y^3z)/9*(45y)/(8x^5z^3)

$\frac{4 x^{2} y^{3} z}{9} \cdot \frac{45 y}{8 x^{5} z^{3}}$

Combine.

$\frac{4 x^{2} y^{3} z (45 y)}{9 (8 x^{5} z^{3})}$

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

Move $y$ .

$\frac{4 x^{2} (y \cdot y^{3}) z \cdot 45}{9 (8 x^{5} z^{3})}$

Multiply $y$ by $y^{3}$ .

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

$\frac{4 x^{2} (y^{1} y^{3}) z \cdot 45}{9 (8 x^{5} z^{3})}$

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

$\frac{4 x^{2} y^{1 + 3} z \cdot 45}{9 (8 x^{5} z^{3})}$

Add $1$ and $3$ .

$\frac{4 x^{2} y^{4} z \cdot 45}{9 (8 x^{5} z^{3})}$

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

Factor $4$ out of $4 x^{2} y^{4} z \cdot 45$ .

$\frac{4 (x^{2} y^{4} z \cdot 45)}{9 (8 x^{5} z^{3})}$

Cancel the common factors.

Factor $4$ out of $9 (8 x^{5} z^{3})$ .

$\frac{4 (x^{2} y^{4} z \cdot 45)}{4 (9 (2 x^{5} z^{3}))}$

Cancel the common factor.

$\frac{4 (x^{2} y^{4} z \cdot 45)}{4 (9 (2 x^{5} z^{3}))}$

Rewrite the expression.

$\frac{x^{2} y^{4} z \cdot 45}{9 (2 x^{5} z^{3})}$

Cancel the common factor of $x^{2}$ and $x^{5}$ .

Factor $x^{2}$ out of $x^{2} y^{4} z \cdot 45$ .

$\frac{x^{2} (y^{4} z \cdot 45)}{9 (2 x^{5} z^{3})}$

Cancel the common factors.

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

$\frac{x^{2} (y^{4} z \cdot 45)}{x^{2} (9 (2 x^{3} z^{3}))}$

Cancel the common factor.

$\frac{x^{2} (y^{4} z \cdot 45)}{x^{2} (9 (2 x^{3} z^{3}))}$

Rewrite the expression.

$\frac{y^{4} z \cdot 45}{9 (2 x^{3} z^{3})}$

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

Factor $z$ out of $y^{4} z \cdot 45$ .

$\frac{z (y^{4} \cdot 45)}{9 (2 x^{3} z^{3})}$

Cancel the common factors.

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

$\frac{z (y^{4} \cdot 45)}{z (9 (2 x^{3} z^{2}))}$

Cancel the common factor.

$\frac{z (y^{4} \cdot 45)}{z (9 (2 x^{3} z^{2}))}$

Rewrite the expression.

$\frac{y^{4} \cdot 45}{9 (2 x^{3} z^{2})}$

Cancel the common factor of $45$ and $9$ .

Factor $9$ out of $y^{4} \cdot 45$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Move $5$ to the left of $y^{4}$ .

$\frac{5 y^{4}}{2 x^{3} z^{2}}$

Simplify (4x^2y^3z)/9*(45y)/(8x^5z^3)

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