Precalculus Examples

$h^{2} j^{- 3} (2 h j^{4} - h^{- 2} j^{- 1})$

Step 1

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

$h^{2} \frac{1}{j^{3}} (2 h j^{4} - h^{- 2} j^{- 1})$

Step 2

Simplify terms.

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Step 2.1

Combine $h^{2}$ and $\frac{1}{j^{3}}$ .

$\frac{h^{2}}{j^{3}} (2 h j^{4} - h^{- 2} j^{- 1})$

Step 2.2

Simplify each term.

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Step 2.2.1

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

$\frac{h^{2}}{j^{3}} (2 h j^{4} - \frac{1}{h^{2}} j^{- 1})$

Step 2.2.2

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

$\frac{h^{2}}{j^{3}} (2 h j^{4} - \frac{1}{h^{2}} \cdot \frac{1}{j})$

Step 2.2.3

Multiply $\frac{1}{j}$ by $\frac{1}{h^{2}}$ .

$\frac{h^{2}}{j^{3}} (2 h j^{4} - \frac{1}{j h^{2}})$

Step 2.3

Multiply $\frac{h^{2}}{j^{3}}$ by $2 h j^{4} - \frac{1}{j h^{2}}$ .

$\frac{h^{2} (2 h j^{4} - \frac{1}{j h^{2}})}{j^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

To write $2 h j^{4}$ as a fraction with a common denominator, multiply by $\frac{j h^{2}}{j h^{2}}$ .

$\frac{h^{2} (2 h j^{4} \cdot \frac{j h^{2}}{j h^{2}} - \frac{1}{j h^{2}})}{j^{3}}$

Step 3.2

Combine $2 h j^{4}$ and $\frac{j h^{2}}{j h^{2}}$ .

$\frac{h^{2} (\frac{2 h j^{4} (j h^{2})}{j h^{2}} - \frac{1}{j h^{2}})}{j^{3}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{h^{2} \frac{2 h j^{4} (j h^{2}) - 1}{j h^{2}}}{j^{3}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $h$ by $h^{2}$ by adding the exponents.

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Step 3.4.1.1

Move $h^{2}$ .

$\frac{h^{2} \frac{2 (h^{2} h) j^{4} j - 1}{j h^{2}}}{j^{3}}$

Step 3.4.1.2

Multiply $h^{2}$ by $h$ .

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Step 3.4.1.2.1

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

$\frac{h^{2} \frac{2 (h^{2} h^{1}) j^{4} j - 1}{j h^{2}}}{j^{3}}$

Step 3.4.1.2.2

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

$\frac{h^{2} \frac{2 h^{2 + 1} j^{4} j - 1}{j h^{2}}}{j^{3}}$

Step 3.4.1.3

Add $2$ and $1$ .

$\frac{h^{2} \frac{2 h^{3} j^{4} j - 1}{j h^{2}}}{j^{3}}$

Step 3.4.2

Multiply $j^{4}$ by $j$ by adding the exponents.

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Step 3.4.2.1

Move $j$ .

$\frac{h^{2} \frac{2 h^{3} (j \cdot j^{4}) - 1}{j h^{2}}}{j^{3}}$

Step 3.4.2.2

Multiply $j$ by $j^{4}$ .

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Step 3.4.2.2.1

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

$\frac{h^{2} \frac{2 h^{3} (j^{1} j^{4}) - 1}{j h^{2}}}{j^{3}}$

Step 3.4.2.2.2

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

$\frac{h^{2} \frac{2 h^{3} j^{1 + 4} - 1}{j h^{2}}}{j^{3}}$

Step 3.4.2.3

Add $1$ and $4$ .

$\frac{h^{2} \frac{2 h^{3} j^{5} - 1}{j h^{2}}}{j^{3}}$

Step 4

Simplify terms.

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Step 4.1

Combine $h^{2}$ and $\frac{2 h^{3} j^{5} - 1}{j h^{2}}$ .

$\frac{\frac{h^{2} (2 h^{3} j^{5} - 1)}{j h^{2}}}{j^{3}}$

Step 4.2

Reduce the expression $\frac{h^{2} (2 h^{3} j^{5} - 1)}{j h^{2}}$ by cancelling the common factors.

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Step 4.2.1

Cancel the common factor.

$\frac{\frac{h^{2} (2 h^{3} j^{5} - 1)}{j h^{2}}}{j^{3}}$

Step 4.2.2

Rewrite the expression.

$\frac{\frac{2 h^{3} j^{5} - 1}{j}}{j^{3}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 h^{3} j^{5} - 1}{j} \cdot \frac{1}{j^{3}}$

Step 6

Multiply $\frac{2 h^{3} j^{5} - 1}{j} \cdot \frac{1}{j^{3}}$ .

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Step 6.1

Multiply $\frac{2 h^{3} j^{5} - 1}{j}$ by $\frac{1}{j^{3}}$ .

$\frac{2 h^{3} j^{5} - 1}{j \cdot j^{3}}$

Step 6.2

Multiply $j$ by $j^{3}$ by adding the exponents.

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Step 6.2.1

Multiply $j$ by $j^{3}$ .

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Step 6.2.1.1

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

$\frac{2 h^{3} j^{5} - 1}{j^{1} j^{3}}$

Step 6.2.1.2

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

$\frac{2 h^{3} j^{5} - 1}{j^{1 + 3}}$

Step 6.2.2

Add $1$ and $3$ .

$\frac{2 h^{3} j^{5} - 1}{j^{4}}$