Simplify ((x^-1y^0)/(2xy^0))^-3

${(\frac{x^{- 1} y^{0}}{2 x y^{0}})}^{- 3}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{2 x y^{0} x})}^{- 3}$

Step 2

Simplify the denominator.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

${(\frac{1}{2 x^{2} y^{0}})}^{- 3}$

Simplify $2 x^{2} y^{0}$ .

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(2 x^{2})}^{3}$

Step 4

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

$2^{3} {(x^{2})}^{3}$

Step 5

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

$8 {(x^{2})}^{3}$

Step 6

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

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

$8 x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$8 x^{6}$