Algebra Examples

$5 x^{- 3} y^{4} (7 x^{3} + 2 y^{- 4})$

Step 1

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

$5 \frac{1}{x^{3}} y^{4} (7 x^{3} + 2 y^{- 4})$

Step 2

Simplify terms.

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Step 2.1

Combine $5$ and $\frac{1}{x^{3}}$ .

$\frac{5}{x^{3}} y^{4} (7 x^{3} + 2 y^{- 4})$

Step 2.2

Combine $\frac{5}{x^{3}}$ and $y^{4}$ .

$\frac{5 y^{4}}{x^{3}} (7 x^{3} + 2 y^{- 4})$

Step 2.3

Simplify each term.

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Step 2.3.1

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

$\frac{5 y^{4}}{x^{3}} (7 x^{3} + 2 \frac{1}{y^{4}})$

Step 2.3.2

Combine $2$ and $\frac{1}{y^{4}}$ .

$\frac{5 y^{4}}{x^{3}} (7 x^{3} + \frac{2}{y^{4}})$

Step 2.4

Multiply $\frac{5 y^{4}}{x^{3}}$ by $7 x^{3} + \frac{2}{y^{4}}$ .

$\frac{5 y^{4} (7 x^{3} + \frac{2}{y^{4}})}{x^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

To write $7 x^{3}$ as a fraction with a common denominator, multiply by $\frac{y^{4}}{y^{4}}$ .

$\frac{5 y^{4} (\frac{7 x^{3} y^{4}}{y^{4}} + \frac{2}{y^{4}})}{x^{3}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 y^{4} \frac{7 x^{3} y^{4} + 2}{y^{4}}}{x^{3}}$

Step 3.3

Combine exponents.

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Step 3.3.1

Combine $5$ and $\frac{7 x^{3} y^{4} + 2}{y^{4}}$ .

$\frac{y^{4} \frac{5 (7 x^{3} y^{4} + 2)}{y^{4}}}{x^{3}}$

Step 3.3.2

Combine $y^{4}$ and $\frac{5 (7 x^{3} y^{4} + 2)}{y^{4}}$ .

$\frac{\frac{y^{4} (5 (7 x^{3} y^{4} + 2))}{y^{4}}}{x^{3}}$

Step 3.4

Remove unnecessary parentheses.

$\frac{\frac{y^{4} \cdot 5 (7 x^{3} y^{4} + 2)}{y^{4}}}{x^{3}}$

Step 3.5

Reduce the expression by cancelling the common factors.

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Step 3.5.1

Reduce the expression $\frac{y^{4} \cdot 5 (7 x^{3} y^{4} + 2)}{y^{4}}$ by cancelling the common factors.

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Step 3.5.1.1

Cancel the common factor.

$\frac{\frac{y^{4} \cdot 5 (7 x^{3} y^{4} + 2)}{y^{4}}}{x^{3}}$

Step 3.5.1.2

Rewrite the expression.

$\frac{\frac{5 (7 x^{3} y^{4} + 2)}{1}}{x^{3}}$

Step 3.5.2

Divide $5 (7 x^{3} y^{4} + 2)$ by $1$ .

$\frac{5 (7 x^{3} y^{4} + 2)}{x^{3}}$