Algebra Examples

${(\frac{x^{3}}{y^{8}})}^{4} (\frac{2 x^{3} y}{x^{2} y^{5}})$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{x^{3}}{y^{8}}$ .

$\frac{{(x^{3})}^{4}}{{(y^{8})}^{4}} \cdot \frac{2 x^{3} y}{x^{2} y^{5}}$

Step 1.2

Combine.

$\frac{{(x^{3})}^{4} (2 x^{3} y)}{{(y^{8})}^{4} (x^{2} y^{5})}$

Step 1.3

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

Tap for more steps...

Step 1.3.1

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

$\frac{x^{2} ({(x^{3})}^{4} (2 x y))}{{(y^{8})}^{4} (x^{2} y^{5})}$

Step 1.3.2

Cancel the common factors.

Tap for more steps...

Step 1.3.2.1

Factor $x^{2}$ out of ${(y^{8})}^{4} (x^{2} y^{5})$ .

$\frac{x^{2} ({(x^{3})}^{4} (2 x y))}{x^{2} ({(y^{8})}^{4} (y^{5}))}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{2} ({(x^{3})}^{4} (2 x y))}{x^{2} ({(y^{8})}^{4} (y^{5}))}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{(x^{3})}^{4} (2 x y)}{{(y^{8})}^{4} (y^{5})}$

Step 1.4

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

Tap for more steps...

Step 1.4.1

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

$\frac{y ({(x^{3})}^{4} (2 x))}{{(y^{8})}^{4} (y^{5})}$

Step 1.4.2

Cancel the common factors.

Tap for more steps...

Step 1.4.2.1

Factor $y$ out of ${(y^{8})}^{4} (y^{5})$ .

$\frac{y ({(x^{3})}^{4} (2 x))}{y ({(y^{8})}^{4} (y^{4}))}$

Step 1.4.2.2

Cancel the common factor.

$\frac{y ({(x^{3})}^{4} (2 x))}{y ({(y^{8})}^{4} (y^{4}))}$

Step 1.4.2.3

Rewrite the expression.

$\frac{{(x^{3})}^{4} (2 x)}{{(y^{8})}^{4} (y^{4})}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Multiply the exponents in ${(x^{3})}^{4}$ .

Tap for more steps...

Step 2.1.1

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

$\frac{x^{3 \cdot 4} \cdot 2 x}{{(y^{8})}^{4} (y^{4})}$

Step 2.1.2

Multiply $3$ by $4$ .

$\frac{x^{12} \cdot 2 x}{{(y^{8})}^{4} (y^{4})}$

Step 2.2

Combine exponents.

Tap for more steps...

Step 2.2.1

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

$\frac{2 (x^{12} x^{1})}{{(y^{8})}^{4} (y^{4})}$

Step 2.2.2

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

$\frac{2 x^{12 + 1}}{{(y^{8})}^{4} (y^{4})}$

Step 2.2.3

Add $12$ and $1$ .

$\frac{2 x^{13}}{{(y^{8})}^{4} (y^{4})}$

Step 3

Multiply the exponents in ${(y^{8})}^{4}$ .

Tap for more steps...

Step 3.1

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

$\frac{2 x^{13}}{y^{8 \cdot 4} y^{4}}$

Step 3.2

Multiply $8$ by $4$ .

$\frac{2 x^{13}}{y^{32} y^{4}}$

Step 4

Multiply $y^{32}$ by $y^{4}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

$\frac{2 x^{13}}{y^{32 + 4}}$

Step 4.2

Add $32$ and $4$ .

$\frac{2 x^{13}}{y^{36}}$