Simplify (4x^5y^3*(3x^8y^7))/(6x^4y^10)

$\frac{4 x^{5} y^{3} \cdot (3 x^{8} y^{7})}{6 x^{4} y^{10}}$

Step 1

Multiply $x^{5}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$\frac{4 (x^{8} x^{5}) y^{3} \cdot (3 y^{7})}{6 x^{4} y^{10}}$

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

$\frac{4 x^{8 + 5} y^{3} \cdot (3 y^{7})}{6 x^{4} y^{10}}$

Add $8$ and $5$ .

$\frac{4 x^{13} y^{3} \cdot (3 y^{7})}{6 x^{4} y^{10}}$

Step 2

Multiply $y^{3}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$\frac{4 x^{13} (y^{7} y^{3}) \cdot 3}{6 x^{4} y^{10}}$

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

$\frac{4 x^{13} y^{7 + 3} \cdot 3}{6 x^{4} y^{10}}$

Add $7$ and $3$ .

$\frac{4 x^{13} y^{10} \cdot 3}{6 x^{4} y^{10}}$

Step 3

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 x^{13} y^{10} \cdot 3$ .

$\frac{2 (2 x^{13} y^{10} \cdot 3)}{6 x^{4} y^{10}}$

Cancel the common factors.

Factor $2$ out of $6 x^{4} y^{10}$ .

$\frac{2 (2 x^{13} y^{10} \cdot 3)}{2 (3 x^{4} y^{10})}$

Cancel the common factor.

$\frac{2 (2 x^{13} y^{10} \cdot 3)}{2 (3 x^{4} y^{10})}$

Rewrite the expression.

$\frac{2 x^{13} y^{10} \cdot 3}{3 x^{4} y^{10}}$

Step 4

Cancel the common factor of $x^{13}$ and $x^{4}$ .

Factor $x^{4}$ out of $2 x^{13} y^{10} \cdot 3$ .

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

Cancel the common factors.

Factor $x^{4}$ out of $3 x^{4} y^{10}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x^{9} y^{10} \cdot 3}{3 y^{10}}$

Step 5

Cancel the common factor of $y^{10}$ .

Cancel the common factor.

$\frac{2 x^{9} y^{10} \cdot 3}{3 y^{10}}$

Rewrite the expression.

$\frac{2 x^{9} \cdot 3}{3}$

Step 6

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 x^{9} \cdot 3}{3}$

Divide $2 x^{9}$ by $1$ .

$2 x^{9}$

Simplify (4x^5y^3*(3x^8y^7))/(6x^4y^10)

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