Simplify ((2x^0y^3)^-3)/(x^3y^4*2x^2y^0)

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

Step 1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

$\frac{{(2 x^{0} y^{3})}^{- 3}}{x^{5} y^{4} \cdot (2 y^{0})}$

Step 2

Simplify the expression.

Simplify $x^{5} y^{4} \cdot (2 y^{0})$ .

$\frac{{(2 x^{0} y^{3})}^{- 3}}{x^{5} y^{4} \cdot 2}$

Move ${(2 x^{0} y^{3})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{5} y^{4} \cdot 2 {(2 x^{0} y^{3})}^{3}}$

Step 3

Simplify the denominator.

Apply the product rule to $2 x^{0} y^{3}$ .

$\frac{1}{x^{5} y^{4} \cdot 2 {(2 x^{0})}^{3} {(y^{3})}^{3}}$

Anything raised to $0$ is $1$ .

$\frac{1}{x^{5} y^{4} \cdot 2 {(2 \cdot 1)}^{3} {(y^{3})}^{3}}$

Multiply $2$ by $1$ .

$\frac{1}{x^{5} y^{4} \cdot 2 \cdot 2^{3} {(y^{3})}^{3}}$

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

$\frac{1}{x^{5} y^{4} \cdot 2 \cdot 8 {(y^{3})}^{3}}$

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

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

$\frac{1}{x^{5} y^{4} \cdot 2 \cdot 8 y^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{1}{x^{5} y^{4} \cdot 2 \cdot 8 y^{9}}$

Combine exponents.

Multiply $8$ by $2$ .

$\frac{1}{x^{5} y^{4} \cdot 16 y^{9}}$

Multiply $y^{4}$ by $y^{9}$ by adding the exponents.

Move $y^{9}$ .

$\frac{1}{x^{5} (y^{9} y^{4}) \cdot 16}$

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

$\frac{1}{x^{5} y^{9 + 4} \cdot 16}$

Add $9$ and $4$ .

$\frac{1}{x^{5} y^{13} \cdot 16}$

Step 4

Move $16$ to the left of $x^{5} y^{13}$ .

$\frac{1}{16 x^{5} y^{13}}$