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

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

Step 1

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

Move $y^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 5

Cancel the common factor of $y^{4}$ and $y^{3}$ .

Factor $y^{3}$ out of $y^{4} \cdot 2$ .

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

Cancel the common factors.

Factor $y^{3}$ out of $2 x^{4} y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Apply basic rules of exponents.

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

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

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

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

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

Multiply $4$ by $2$ .

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

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

Related Questions

Support LCMGCF.com by disabling your adblocker.