Algebra Examples

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

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

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine

5

$5$ and

\frac{1}{x^{3}}

$\frac{1}{x^{3}}$ .

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

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

Step 2.2

Combine

\frac{5}{x^{3}}

$\frac{5}{x^{3}}$ and

y^{4}

$y^{4}$ .

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

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

Step 2.3

Simplify each term.

Tap for more steps...

Step 2.3.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 2.3.2

Combine

2

$2$ and

\frac{1}{y^{4}}

$\frac{1}{y^{4}}$ .

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

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

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

$\frac{5 y^{4}}{x^{3}}$ by

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

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

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

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

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

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

To write

7 x^{3}

$7 x^{3}$ as a fraction with a common denominator, multiply by

\frac{y^{4}}{y^{4}}

$\frac{y^{4}}{y^{4}}$ .

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

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

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}}

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

Step 3.3

Combine exponents.

Tap for more steps...

Step 3.3.1

Combine

5

$5$ and

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

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

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

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

Step 3.3.2

Combine

y^{4}

$y^{4}$ and

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

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

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

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

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

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

Step 3.4

Remove unnecessary parentheses.

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

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

Step 3.5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.5.1

Reduce the expression

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

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

Tap for more steps...

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

$1$ .

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