Simplify (15x^3y^4)/(21x^2y^2)*(14x^2y^3)/(6xy^2)

$\frac{15 x^{3} y^{4}}{21 x^{2} y^{2}} \cdot \frac{14 x^{2} y^{3}}{6 x y^{2}}$

Step 1

Combine.

$\frac{15 x^{3} y^{4} (14 x^{2} y^{3})}{21 x^{2} y^{2} (6 x y^{2})}$

Step 2

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

Move $x^{2}$ .

$\frac{15 (x^{2} x^{3}) y^{4} (14 y^{3})}{21 x^{2} y^{2} (6 x y^{2})}$

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

$\frac{15 x^{2 + 3} y^{4} (14 y^{3})}{21 x^{2} y^{2} (6 x y^{2})}$

Add $2$ and $3$ .

$\frac{15 x^{5} y^{4} (14 y^{3})}{21 x^{2} y^{2} (6 x y^{2})}$

Step 3

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{15 x^{5} (y^{3} y^{4}) \cdot 14}{21 x^{2} y^{2} (6 x y^{2})}$

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

$\frac{15 x^{5} y^{3 + 4} \cdot 14}{21 x^{2} y^{2} (6 x y^{2})}$

Add $3$ and $4$ .

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{2} y^{2} (6 x y^{2})}$

Step 4

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

Move $x$ .

$\frac{15 x^{5} y^{7} \cdot 14}{21 (x \cdot x^{2}) y^{2} (6 y^{2})}$

Multiply $x$ by $x^{2}$ .

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

$\frac{15 x^{5} y^{7} \cdot 14}{21 (x^{1} x^{2}) y^{2} (6 y^{2})}$

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

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{1 + 2} y^{2} (6 y^{2})}$

Add $1$ and $2$ .

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{3} y^{2} (6 y^{2})}$

Step 5

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

Move $y^{2}$ .

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{3} (y^{2} y^{2}) \cdot 6}$

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

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{3} y^{2 + 2} \cdot 6}$

Add $2$ and $2$ .

$\frac{15 x^{5} y^{7} \cdot 14}{21 x^{3} y^{4} \cdot 6}$

Step 6

Cancel the common factor of $15$ and $21$ .

Factor $3$ out of $15 x^{5} y^{7} \cdot 14$ .

$\frac{3 (5 x^{5} y^{7} \cdot 14)}{21 x^{3} y^{4} \cdot 6}$

Cancel the common factors.

Factor $3$ out of $21 x^{3} y^{4} \cdot 6$ .

$\frac{3 (5 x^{5} y^{7} \cdot 14)}{3 (7 x^{3} y^{4} \cdot 6)}$

Cancel the common factor.

$\frac{3 (5 x^{5} y^{7} \cdot 14)}{3 (7 x^{3} y^{4} \cdot 6)}$

Rewrite the expression.

$\frac{5 x^{5} y^{7} \cdot 14}{7 x^{3} y^{4} \cdot 6}$

Step 7

Cancel the common factor of $x^{5}$ and $x^{3}$ .

Factor $x^{3}$ out of $5 x^{5} y^{7} \cdot 14$ .

$\frac{x^{3} (5 x^{2} y^{7} \cdot 14)}{7 x^{3} y^{4} \cdot 6}$

Cancel the common factors.

Factor $x^{3}$ out of $7 x^{3} y^{4} \cdot 6$ .

$\frac{x^{3} (5 x^{2} y^{7} \cdot 14)}{x^{3} (7 y^{4} \cdot 6)}$

Cancel the common factor.

$\frac{x^{3} (5 x^{2} y^{7} \cdot 14)}{x^{3} (7 y^{4} \cdot 6)}$

Rewrite the expression.

$\frac{5 x^{2} y^{7} \cdot 14}{7 y^{4} \cdot 6}$

Step 8

Cancel the common factor of $y^{7}$ and $y^{4}$ .

Factor $y^{4}$ out of $5 x^{2} y^{7} \cdot 14$ .

$\frac{y^{4} (5 x^{2} y^{3} \cdot 14)}{7 y^{4} \cdot 6}$

Cancel the common factors.

Factor $y^{4}$ out of $7 y^{4} \cdot 6$ .

$\frac{y^{4} (5 x^{2} y^{3} \cdot 14)}{y^{4} (7 \cdot 6)}$

Cancel the common factor.

$\frac{y^{4} (5 x^{2} y^{3} \cdot 14)}{y^{4} (7 \cdot 6)}$

Rewrite the expression.

$\frac{5 x^{2} y^{3} \cdot 14}{7 \cdot 6}$

Step 9

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $5 x^{2} y^{3} \cdot 14$ .

$\frac{7 (5 x^{2} y^{3} \cdot 2)}{7 \cdot 6}$

Cancel the common factors.

Factor $7$ out of $7 \cdot 6$ .

$\frac{7 (5 x^{2} y^{3} \cdot 2)}{7 (6)}$

Cancel the common factor.

$\frac{7 (5 x^{2} y^{3} \cdot 2)}{7 \cdot 6}$

Rewrite the expression.

$\frac{5 x^{2} y^{3} \cdot 2}{6}$

Step 10

Cancel the common factor of $2$ and $6$ .

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

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (15x^3y^4)/(21x^2y^2)*(14x^2y^3)/(6xy^2)

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