Simplify (27x^2y^4)/(16yz^3)*(8z)/(9xy^3)

$\frac{27 x^{2} y^{4}}{16 y z^{3}} \cdot \frac{8 z}{9 x y^{3}}$

Step 1

Combine.

$\frac{27 x^{2} y^{4} (8 z)}{16 y z^{3} (9 x y^{3})}$

Step 2

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

Move $y^{3}$ .

$\frac{27 x^{2} y^{4} (8 z)}{16 (y^{3} y) z^{3} (9 x)}$

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

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

$\frac{27 x^{2} y^{4} (8 z)}{16 (y^{3} y^{1}) z^{3} (9 x)}$

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

$\frac{27 x^{2} y^{4} (8 z)}{16 y^{3 + 1} z^{3} (9 x)}$

Add $3$ and $1$ .

$\frac{27 x^{2} y^{4} (8 z)}{16 y^{4} z^{3} (9 x)}$

Step 3

Cancel the common factor of $27$ and $9$ .

Factor $9$ out of $27 x^{2} y^{4} (8 z)$ .

$\frac{9 (3 x^{2} y^{4} (8 z))}{16 y^{4} z^{3} (9 x)}$

Cancel the common factors.

Factor $9$ out of $16 y^{4} z^{3} (9 x)$ .

$\frac{9 (3 x^{2} y^{4} (8 z))}{9 (16 y^{4} z^{3} (x))}$

Cancel the common factor.

$\frac{9 (3 x^{2} y^{4} (8 z))}{9 (16 y^{4} z^{3} (x))}$

Rewrite the expression.

$\frac{3 x^{2} y^{4} (8 z)}{16 y^{4} z^{3} (x)}$

Step 4

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

Factor $x$ out of $3 x^{2} y^{4} (8 z)$ .

$\frac{x (3 x y^{4} (8 z))}{16 y^{4} z^{3} (x)}$

Cancel the common factors.

Factor $x$ out of $16 y^{4} z^{3} (x)$ .

$\frac{x (3 x y^{4} (8 z))}{x (16 y^{4} z^{3})}$

Cancel the common factor.

$\frac{x (3 x y^{4} (8 z))}{x (16 y^{4} z^{3})}$

Rewrite the expression.

$\frac{3 x y^{4} (8 z)}{16 y^{4} z^{3}}$

Step 5

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

Cancel the common factor.

$\frac{3 x y^{4} (8 z)}{16 y^{4} z^{3}}$

Rewrite the expression.

$\frac{3 x (8 z)}{16 z^{3}}$

Step 6

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $3 x (8 z)$ .

$\frac{8 (3 x (z))}{16 z^{3}}$

Cancel the common factors.

Factor $8$ out of $16 z^{3}$ .

$\frac{8 (3 x (z))}{8 (2 z^{3})}$

Cancel the common factor.

$\frac{8 (3 x (z))}{8 (2 z^{3})}$

Rewrite the expression.

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

Step 7

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

Factor $z$ out of $3 x (z)$ .

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

Cancel the common factors.

Factor $z$ out of $2 z^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 x}{2 z^{2}}$

Simplify (27x^2y^4)/(16yz^3)*(8z)/(9xy^3)

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