Simplify (10x^3)/(8y^3)(16x)/(15y^2)(9y^4)/(x^3)

$\frac{10 x^{3}}{8 y^{3}} \cdot \frac{16 x}{15 y^{2}} \cdot \frac{9 y^{4}}{x^{3}}$

Step 1

Combine.

$\frac{10 x^{3} (16 x)}{8 y^{3} (15 y^{2})} \cdot \frac{9 y^{4}}{x^{3}}$

Step 2

Combine.

$\frac{10 x^{3} (16 x) (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 3

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

Move $x$ .

$\frac{10 (x \cdot x^{3}) \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

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

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

$\frac{10 (x^{1} x^{3}) \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

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

$\frac{10 x^{1 + 3} \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Add $1$ and $3$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{3} (15 y^{2}) x^{3}}$

Step 4

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 (y^{2} y^{3}) \cdot 15 x^{3}}$

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

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{2 + 3} \cdot 15 x^{3}}$

Add $2$ and $3$ .

$\frac{10 x^{4} \cdot 16 (9 y^{4})}{8 y^{5} \cdot 15 x^{3}}$

Step 5

Cancel the common factor of $10$ and $8$ .

Factor $2$ out of $10 x^{4} \cdot 16 (9 y^{4})$ .

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{8 y^{5} \cdot 15 x^{3}}$

Cancel the common factors.

Factor $2$ out of $8 y^{5} \cdot 15 x^{3}$ .

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{2 (4 y^{5} \cdot 15 x^{3})}$

Cancel the common factor.

$\frac{2 (5 x^{4} \cdot 16 (9 y^{4}))}{2 (4 y^{5} \cdot 15 x^{3})}$

Rewrite the expression.

$\frac{5 x^{4} \cdot 16 (9 y^{4})}{4 y^{5} \cdot 15 x^{3}}$

Step 6

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 x^{4} \cdot 16 (9 y^{4})$ .

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{4 y^{5} \cdot 15 x^{3}}$

Cancel the common factors.

Factor $5$ out of $4 y^{5} \cdot 15 x^{3}$ .

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{5 (4 y^{5} \cdot 3 x^{3})}$

Cancel the common factor.

$\frac{5 (x^{4} \cdot 16 (9 y^{4}))}{5 (4 y^{5} \cdot 3 x^{3})}$

Rewrite the expression.

$\frac{x^{4} \cdot 16 (9 y^{4})}{4 y^{5} \cdot 3 x^{3}}$

Step 7

Cancel the common factor of $x^{4}$ and $x^{3}$ .

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

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{4 y^{5} \cdot 3 x^{3}}$

Cancel the common factors.

Factor $x^{3}$ out of $4 y^{5} \cdot 3 x^{3}$ .

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{x^{3} (4 y^{5} \cdot 3)}$

Cancel the common factor.

$\frac{x^{3} (x \cdot 16 (9 y^{4}))}{x^{3} (4 y^{5} \cdot 3)}$

Rewrite the expression.

$\frac{x \cdot 16 (9 y^{4})}{4 y^{5} \cdot 3}$

Step 8

Cancel the common factor of $16$ and $4$ .

Factor $4$ out of $x \cdot 16 (9 y^{4})$ .

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

Cancel the common factors.

Factor $4$ out of $4 y^{5} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

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

Factor $3$ out of $x \cdot 4 (9 y^{4})$ .

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

Cancel the common factors.

Factor $3$ out of $y^{5} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 10

Cancel the common factor of $y^{4}$ and $y^{5}$ .

Factor $y^{4}$ out of $x \cdot 4 (3 y^{4})$ .

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

Cancel the common factors.

Factor $y^{4}$ out of $y^{5}$ .

$\frac{y^{4} (x \cdot 4 \cdot (3))}{y^{4} y}$

Cancel the common factor.

$\frac{y^{4} (x \cdot 4 \cdot (3))}{y^{4} y}$

Rewrite the expression.

$\frac{x \cdot 4 \cdot (3)}{y}$

Step 11

Simplify the expression.

Multiply $3$ by $4$ .

$\frac{x \cdot 12}{y}$

Move $12$ to the left of $x$ .

$\frac{12 x}{y}$

Simplify (10x^3)/(8y^3)*(16x)/(15y^2)*(9y^4)/(x^3)

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Simplify (10x^3)/(8y^3)(16x)/(15y^2)(9y^4)/(x^3)