Simplify ((2^3x^3y^2)^3)/((2^4x^2y^4)^2)

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

Step 1

Simplify the numerator.

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

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

Raise $2$ to the power of $3$ .

$\frac{{(8 x^{3})}^{3} {(y^{2})}^{3}}{{(2^{4} x^{2} y^{4})}^{2}}$

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

$\frac{8^{3} {(x^{3})}^{3} {(y^{2})}^{3}}{{(2^{4} x^{2} y^{4})}^{2}}$

Raise $8$ to the power of $3$ .

$\frac{512 {(x^{3})}^{3} {(y^{2})}^{3}}{{(2^{4} x^{2} y^{4})}^{2}}$

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

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

$\frac{512 x^{3 \cdot 3} {(y^{2})}^{3}}{{(2^{4} x^{2} y^{4})}^{2}}$

Multiply $3$ by $3$ .

$\frac{512 x^{9} {(y^{2})}^{3}}{{(2^{4} x^{2} y^{4})}^{2}}$

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

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

$\frac{512 x^{9} y^{2 \cdot 3}}{{(2^{4} x^{2} y^{4})}^{2}}$

Multiply $2$ by $3$ .

$\frac{512 x^{9} y^{6}}{{(2^{4} x^{2} y^{4})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $2^{4} x^{2} y^{4}$ .

$\frac{512 x^{9} y^{6}}{{(2^{4} x^{2})}^{2} {(y^{4})}^{2}}$

Raise $2$ to the power of $4$ .

$\frac{512 x^{9} y^{6}}{{(16 x^{2})}^{2} {(y^{4})}^{2}}$

Apply the product rule to $16 x^{2}$ .

$\frac{512 x^{9} y^{6}}{16^{2} {(x^{2})}^{2} {(y^{4})}^{2}}$

Raise $16$ to the power of $2$ .

$\frac{512 x^{9} y^{6}}{256 {(x^{2})}^{2} {(y^{4})}^{2}}$

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

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

$\frac{512 x^{9} y^{6}}{256 x^{2 \cdot 2} {(y^{4})}^{2}}$

Multiply $2$ by $2$ .

$\frac{512 x^{9} y^{6}}{256 x^{4} {(y^{4})}^{2}}$

Multiply the exponents in ${(y^{4})}^{2}$ .

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

$\frac{512 x^{9} y^{6}}{256 x^{4} y^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{512 x^{9} y^{6}}{256 x^{4} y^{8}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $512$ and $256$ .

Factor $256$ out of $512 x^{9} y^{6}$ .

$\frac{256 (2 x^{9} y^{6})}{256 x^{4} y^{8}}$

Cancel the common factors.

Factor $256$ out of $256 x^{4} y^{8}$ .

$\frac{256 (2 x^{9} y^{6})}{256 (x^{4} y^{8})}$

Cancel the common factor.

$\frac{256 (2 x^{9} y^{6})}{256 (x^{4} y^{8})}$

Rewrite the expression.

$\frac{2 x^{9} y^{6}}{x^{4} y^{8}}$

Cancel the common factor of $x^{9}$ and $x^{4}$ .

Factor $x^{4}$ out of $2 x^{9} y^{6}$ .

$\frac{x^{4} (2 x^{5} y^{6})}{x^{4} y^{8}}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{4} y^{8}$ .

$\frac{x^{4} (2 x^{5} y^{6})}{x^{4} (y^{8})}$

Cancel the common factor.

$\frac{x^{4} (2 x^{5} y^{6})}{x^{4} y^{8}}$

Rewrite the expression.

$\frac{2 x^{5} y^{6}}{y^{8}}$

Cancel the common factor of $y^{6}$ and $y^{8}$ .

Factor $y^{6}$ out of $2 x^{5} y^{6}$ .

$\frac{y^{6} (2 x^{5})}{y^{8}}$

Cancel the common factors.

Factor $y^{6}$ out of $y^{8}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((2^3x^3y^2)^3)/((2^4x^2y^4)^2)

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