Simplify (16(x^3y)^2)/(2(xy^0)^4)

$\frac{16 {(x^{3} y)}^{2}}{2 {(x y^{0})}^{4}}$

Step 1

Cancel the common factor of $16$ and $2$ .

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

$\frac{2 (8 {(x^{3} y)}^{2})}{2 {(x y^{0})}^{4}}$

Cancel the common factors.

Factor $2$ out of $2 {(x y^{0})}^{4}$ .

$\frac{2 (8 {(x^{3} y)}^{2})}{2 ({(x y^{0})}^{4})}$

Cancel the common factor.

$\frac{2 (8 {(x^{3} y)}^{2})}{2 {(x y^{0})}^{4}}$

Rewrite the expression.

$\frac{8 {(x^{3} y)}^{2}}{{(x y^{0})}^{4}}$

Step 2

Simplify the numerator.

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

$\frac{8 {(x^{3})}^{2} y^{2}}{{(x y^{0})}^{4}}$

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

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

$\frac{8 x^{3 \cdot 2} y^{2}}{{(x y^{0})}^{4}}$

Multiply $3$ by $2$ .

$\frac{8 x^{6} y^{2}}{{(x y^{0})}^{4}}$

Step 3

Simplify the denominator.

Apply the product rule to $x y^{0}$ .

$\frac{8 x^{6} y^{2}}{x^{4} {(y^{0})}^{4}}$

Multiply the exponents in ${(y^{0})}^{4}$ .

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

$\frac{8 x^{6} y^{2}}{x^{4} y^{0 \cdot 4}}$

Multiply $0$ by $4$ .

$\frac{8 x^{6} y^{2}}{x^{4} y^{0}}$

Anything raised to $0$ is $1$ .

$\frac{8 x^{6} y^{2}}{x^{4} \cdot 1}$

Step 4

Reduce the expression by cancelling the common factors.

Multiply $x^{4}$ by $1$ .

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

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $8 x^{6} y^{2}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{4} (8 x^{2} y^{2})}{x^{4} \cdot 1}$

Cancel the common factor.

$\frac{x^{4} (8 x^{2} y^{2})}{x^{4} \cdot 1}$

Rewrite the expression.

$\frac{8 x^{2} y^{2}}{1}$

Divide $8 x^{2} y^{2}$ by $1$ .

$8 x^{2} y^{2}$

Simplify (16(x^3y)^2)/(2(xy^0)^4)

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