Simplify ((-8x^3y^2)^2*2x^2y^6)/(32x^8y^3)

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot 2 x^{2} y^{6}}{32 x^{8} y^{3}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $32$ .

Factor $2$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (2 x^{2} y^{6})$ .

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{32 x^{8} y^{3}}$

Cancel the common factors.

Factor $2$ out of $32 x^{8} y^{3}$ .

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{2 (16 x^{8} y^{3})}$

Cancel the common factor.

$\frac{2 ({(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6}))}{2 (16 x^{8} y^{3})}$

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6})}{16 x^{8} y^{3}}$

Cancel the common factor of $x^{2}$ and $x^{8}$ .

Factor $x^{2}$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (x^{2} y^{6})$ .

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{16 x^{8} y^{3}}$

Cancel the common factors.

Factor $x^{2}$ out of $16 x^{8} y^{3}$ .

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{x^{2} (16 x^{6} y^{3})}$

Cancel the common factor.

$\frac{x^{2} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{6}))}{x^{2} (16 x^{6} y^{3})}$

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (y^{6})}{16 x^{6} y^{3}}$

Cancel the common factor of $y^{6}$ and $y^{3}$ .

Factor $y^{3}$ out of ${(- 8 x^{3} y^{2})}^{2} \cdot (y^{6})$ .

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{16 x^{6} y^{3}}$

Cancel the common factors.

Factor $y^{3}$ out of $16 x^{6} y^{3}$ .

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{y^{3} (16 x^{6})}$

Cancel the common factor.

$\frac{y^{3} ({(- 8 x^{3} y^{2})}^{2} \cdot (y^{3}))}{y^{3} (16 x^{6})}$

Rewrite the expression.

$\frac{{(- 8 x^{3} y^{2})}^{2} \cdot (y^{3})}{16 x^{6}}$

Step 2

Simplify the numerator.

Apply the product rule to $- 8 x^{3} y^{2}$ .

$\frac{{(- 8 x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Apply the product rule to $- 8 x^{3}$ .

$\frac{{(- 8)}^{2} {(x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Raise $- 8$ to the power of $2$ .

$\frac{64 {(x^{3})}^{2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Multiply the exponents in ${(x^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{64 x^{3 \cdot 2} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Multiply $3$ by $2$ .

$\frac{64 x^{6} {(y^{2})}^{2} y^{3}}{16 x^{6}}$

Multiply the exponents in ${(y^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{64 x^{6} y^{2 \cdot 2} y^{3}}{16 x^{6}}$

Multiply $2$ by $2$ .

$\frac{64 x^{6} y^{4} y^{3}}{16 x^{6}}$

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

Move $y^{3}$ .

$\frac{64 x^{6} (y^{3} y^{4})}{16 x^{6}}$

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

$\frac{64 x^{6} y^{3 + 4}}{16 x^{6}}$

Add $3$ and $4$ .

$\frac{64 x^{6} y^{7}}{16 x^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $64$ and $16$ .

Factor $16$ out of $64 x^{6} y^{7}$ .

$\frac{16 (4 x^{6} y^{7})}{16 x^{6}}$

Cancel the common factors.

Factor $16$ out of $16 x^{6}$ .

$\frac{16 (4 x^{6} y^{7})}{16 (x^{6})}$

Cancel the common factor.

$\frac{16 (4 x^{6} y^{7})}{16 x^{6}}$

Rewrite the expression.

$\frac{4 x^{6} y^{7}}{x^{6}}$

Cancel the common factor of $x^{6}$ .

Cancel the common factor.

$\frac{4 x^{6} y^{7}}{x^{6}}$

Divide $4 y^{7}$ by $1$ .

$4 y^{7}$

Simplify ((-8x^3y^2)^2*2x^2y^6)/(32x^8y^3)

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