Algebra Examples

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

Step 1

Cancel the common factor of $x^{5}$ and $x^{3}$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

$\frac{x^{6}}{2^{3} {(y^{3})}^{3}}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

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

$\frac{x^{6}}{8 {(y^{3})}^{3}}$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$\frac{x^{6}}{8 y^{3 \cdot 3}}$

Step 5.2.2

Multiply $3$ by $3$ .

$\frac{x^{6}}{8 y^{9}}$