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

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

Step 1

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

Move $y^{3}$ .

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

Multiply $y^{3}$ by $y$ .

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

$\frac{{(2 x^{2} y^{2})}^{4}}{y^{3} y^{1} x^{4}}$

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

$\frac{{(2 x^{2} y^{2})}^{4}}{y^{3 + 1} x^{4}}$

Add $3$ and $1$ .

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

Step 2

Simplify the numerator.

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

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

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

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

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

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

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

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

$\frac{16 x^{2 \cdot 4} {(y^{2})}^{4}}{y^{4} x^{4}}$

Multiply $2$ by $4$ .

$\frac{16 x^{8} {(y^{2})}^{4}}{y^{4} x^{4}}$

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

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

$\frac{16 x^{8} y^{2 \cdot 4}}{y^{4} x^{4}}$

Multiply $2$ by $4$ .

$\frac{16 x^{8} y^{8}}{y^{4} x^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{8}$ and $x^{4}$ .

Factor $x^{4}$ out of $16 x^{8} y^{8}$ .

$\frac{x^{4} (16 x^{4} y^{8})}{y^{4} x^{4}}$

Cancel the common factors.

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

$\frac{x^{4} (16 x^{4} y^{8})}{x^{4} y^{4}}$

Cancel the common factor.

$\frac{x^{4} (16 x^{4} y^{8})}{x^{4} y^{4}}$

Rewrite the expression.

$\frac{16 x^{4} y^{8}}{y^{4}}$

Cancel the common factor of $y^{8}$ and $y^{4}$ .

Factor $y^{4}$ out of $16 x^{4} y^{8}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{4} (16 x^{4} y^{4})}{y^{4} \cdot 1}$

Cancel the common factor.

$\frac{y^{4} (16 x^{4} y^{4})}{y^{4} \cdot 1}$

Rewrite the expression.

$\frac{16 x^{4} y^{4}}{1}$

Divide $16 x^{4} y^{4}$ by $1$ .

$16 x^{4} y^{4}$

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

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