Algebra Examples

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

Step 1

Multiply $2 x (\frac{1}{3})$ .

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Step 1.1

Combine $2$ and $\frac{1}{3}$ .

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

Step 1.2

Combine $x$ and $\frac{2}{3}$ .

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Combine $x$ and $\frac{1}{5}$ .

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

Step 5

Combine $\frac{x}{5}$ and $2$ .

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

Step 6

Move $2$ to the left of $x$ .

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

Step 7

Combine $\frac{2 x}{5}$ and $y$ .

${(\frac{2 x y}{5})}^{2}$

Step 8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.1

Apply the product rule to $\frac{2 x y}{5}$ .

$\frac{{(2 x y)}^{2}}{5^{2}}$

Step 8.2

Apply the product rule to $2 x y$ .

$\frac{{(2 x)}^{2} y^{2}}{5^{2}}$

Step 8.3

Apply the product rule to $2 x$ .

$\frac{2^{2} x^{2} y^{2}}{5^{2}}$

Step 9

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

$\frac{4 x^{2} y^{2}}{5^{2}}$

Step 10

Raise $5$ to the power of $2$ .

$\frac{4 x^{2} y^{2}}{25}$