Simplify (4x^3*2x^4y^10)/(50x^9y^4)

$\frac{4 x^{3} \cdot 2 x^{4} y^{10}}{50 x^{9} y^{4}}$

Step 1

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

Move $x^{4}$ .

$\frac{4 (x^{4} x^{3}) \cdot (2 y^{10})}{50 x^{9} y^{4}}$

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

$\frac{4 x^{4 + 3} \cdot (2 y^{10})}{50 x^{9} y^{4}}$

Add $4$ and $3$ .

$\frac{4 x^{7} \cdot (2 y^{10})}{50 x^{9} y^{4}}$

Step 2

Cancel the common factor of $4$ and $50$ .

Factor $2$ out of $4 x^{7} \cdot (2 y^{10})$ .

$\frac{2 (2 x^{7} \cdot (2 y^{10}))}{50 x^{9} y^{4}}$

Cancel the common factors.

Factor $2$ out of $50 x^{9} y^{4}$ .

$\frac{2 (2 x^{7} \cdot (2 y^{10}))}{2 (25 x^{9} y^{4})}$

Cancel the common factor.

$\frac{2 (2 x^{7} \cdot (2 y^{10}))}{2 (25 x^{9} y^{4})}$

Rewrite the expression.

$\frac{2 x^{7} \cdot (2 y^{10})}{25 x^{9} y^{4}}$

Step 3

Cancel the common factor of $x^{7}$ and $x^{9}$ .

Factor $x^{7}$ out of $2 x^{7} \cdot (2 y^{10})$ .

$\frac{x^{7} (2 \cdot (2 y^{10}))}{25 x^{9} y^{4}}$

Cancel the common factors.

Factor $x^{7}$ out of $25 x^{9} y^{4}$ .

$\frac{x^{7} (2 \cdot (2 y^{10}))}{x^{7} (25 x^{2} y^{4})}$

Cancel the common factor.

$\frac{x^{7} (2 \cdot (2 y^{10}))}{x^{7} (25 x^{2} y^{4})}$

Rewrite the expression.

$\frac{2 \cdot (2 y^{10})}{25 x^{2} y^{4}}$

Step 4

Cancel the common factor of $y^{10}$ and $y^{4}$ .

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

$\frac{y^{4} (2 \cdot (2 y^{6}))}{25 x^{2} y^{4}}$

Cancel the common factors.

Factor $y^{4}$ out of $25 x^{2} y^{4}$ .

$\frac{y^{4} (2 \cdot (2 y^{6}))}{y^{4} (25 x^{2})}$

Cancel the common factor.

$\frac{y^{4} (2 \cdot (2 y^{6}))}{y^{4} (25 x^{2})}$

Rewrite the expression.

$\frac{2 \cdot (2 y^{6})}{25 x^{2}}$

Step 5

Simplify the expression.

Multiply $2$ by $2$ .

$\frac{2^{2} y^{6}}{25 x^{2}}$

Raise $2$ to the power of $2$ .

$\frac{4 y^{6}}{25 x^{2}}$

Simplify (4x^3*2x^4y^10)/(50x^9y^4)

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