Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $2 y x^{- 1}$ .

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

Step 1.2

Apply the product rule to $2 y$ .

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

Step 1.3

Raise $2$ to the power of $4$ .

$\frac{2 x^{3} y^{4}}{16 y^{4} {(x^{- 1})}^{4}}$

Step 1.4

Multiply the exponents in ${(x^{- 1})}^{4}$ .

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Step 1.4.1

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

$\frac{2 x^{3} y^{4}}{16 y^{4} x^{- 1 \cdot 4}}$

Step 1.4.2

Multiply $- 1$ by $4$ .

$\frac{2 x^{3} y^{4}}{16 y^{4} x^{- 4}}$

Step 1.5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 x^{3} y^{4}}{16 y^{4} \frac{1}{x^{4}}}$

Step 1.6

Combine exponents.

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Step 1.6.1

Combine $16$ and $\frac{1}{x^{4}}$ .

$\frac{2 x^{3} y^{4}}{y^{4} \frac{16}{x^{4}}}$

Step 1.6.2

Combine $y^{4}$ and $\frac{16}{x^{4}}$ .

$\frac{2 x^{3} y^{4}}{\frac{y^{4} \cdot 16}{x^{4}}}$

Step 1.7

Move $16$ to the left of $y^{4}$ .

$\frac{2 x^{3} y^{4}}{\frac{16 y^{4}}{x^{4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$2 x^{3} y^{4} \frac{x^{4}}{16 y^{4}}$

Step 3

Cancel the common factor of $2 y^{4}$ .

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Step 3.1

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

$2 y^{4} (x^{3}) \frac{x^{4}}{16 y^{4}}$

Step 3.2

Factor $2 y^{4}$ out of $16 y^{4}$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$x^{3} \frac{x^{4}}{8}$

Step 4

Combine $x^{3}$ and $\frac{x^{4}}{8}$ .

$\frac{x^{3} x^{4}}{8}$

Step 5

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 5.1

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

$\frac{x^{3 + 4}}{8}$

Step 5.2

Add $3$ and $4$ .

$\frac{x^{7}}{8}$