Algebra Examples

${(\frac{5 x}{y})}^{2} (\frac{y^{3}}{10 x^{2}})$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{{(5 x)}^{2}}{y^{2}} \cdot \frac{y^{3}}{10 x^{2}}$

Step 1.2

Apply the product rule to $5 x$ .

$\frac{5^{2} x^{2}}{y^{2}} \cdot \frac{y^{3}}{10 x^{2}}$

Step 2

Combine.

$\frac{5^{2} x^{2} y^{3}}{y^{2} (10 x^{2})}$

Step 3

Cancel the common factor of $x^{2}$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{5^{2} x^{2} y^{3}}{y^{2} (10 x^{2})}$

Step 3.2

Rewrite the expression.

$\frac{5^{2} y^{3}}{y^{2} \cdot (10)}$

Step 4

Cancel the common factor of $y^{3}$ and $y^{2}$ .

Tap for more steps...

Step 4.1

Factor $y^{2}$ out of $5^{2} y^{3}$ .

$\frac{y^{2} (5^{2} y)}{y^{2} \cdot (10)}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $y^{2}$ out of $y^{2} \cdot (10)$ .

$\frac{y^{2} (5^{2} y)}{y^{2} (10)}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} (5^{2} y)}{y^{2} \cdot 10}$

Step 4.2.3

Rewrite the expression.

$\frac{5^{2} y}{10}$

Step 5

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

$\frac{25 y}{10}$

Step 6

Cancel the common factor of $25$ and $10$ .

Tap for more steps...

Step 6.1

Factor $5$ out of $25 y$ .

$\frac{5 (5 y)}{10}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $5$ out of $10$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{5 y}{2}$