Pre-Algebra Examples

$7 x^{- 1 - 2} - \frac{9 x^{- 1}}{7^{2} x^{- 2}}$

Step 1

Simplify each term.

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Step 1.1

Subtract $2$ from $- 1$ .

$7 x^{- 3} - \frac{9 x^{- 1}}{7^{2} x^{- 2}}$

Step 1.2

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

$7 \frac{1}{x^{3}} - \frac{9 x^{- 1}}{7^{2} x^{- 2}}$

Step 1.3

Combine $7$ and $\frac{1}{x^{3}}$ .

$\frac{7}{x^{3}} - \frac{9 x^{- 1}}{7^{2} x^{- 2}}$

Step 1.4

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{7}{x^{3}} - \frac{9 x^{- 1} x^{2}}{7^{2}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $x^{- 1}$ by $x^{2}$ by adding the exponents.

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Step 1.5.1.1

Move $x^{2}$ .

$\frac{7}{x^{3}} - \frac{9 (x^{2} x^{- 1})}{7^{2}}$

Step 1.5.1.2

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

$\frac{7}{x^{3}} - \frac{9 x^{2 - 1}}{7^{2}}$

Step 1.5.1.3

Subtract $1$ from $2$ .

$\frac{7}{x^{3}} - \frac{9 x^{1}}{7^{2}}$

Step 1.5.2

Simplify $9 x^{1}$ .

$\frac{7}{x^{3}} - \frac{9 x}{7^{2}}$

Step 1.6

Raise $7$ to the power of $2$ .

$\frac{7}{x^{3}} - \frac{9 x}{49}$

Step 2

To write $\frac{7}{x^{3}}$ as a fraction with a common denominator, multiply by $\frac{49}{49}$ .

$\frac{7}{x^{3}} \cdot \frac{49}{49} - \frac{9 x}{49}$

Step 3

To write $- \frac{9 x}{49}$ as a fraction with a common denominator, multiply by $\frac{x^{3}}{x^{3}}$ .

$\frac{7}{x^{3}} \cdot \frac{49}{49} - \frac{9 x}{49} \cdot \frac{x^{3}}{x^{3}}$

Step 4

Write each expression with a common denominator of $49 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{x^{3}}$ by $\frac{49}{49}$ .

$\frac{7 \cdot 49}{x^{3} \cdot 49} - \frac{9 x}{49} \cdot \frac{x^{3}}{x^{3}}$

Step 4.2

Multiply $\frac{9 x}{49}$ by $\frac{x^{3}}{x^{3}}$ .

$\frac{7 \cdot 49}{x^{3} \cdot 49} - \frac{9 x \cdot x^{3}}{49 x^{3}}$

Step 4.3

Reorder the factors of $x^{3} \cdot 49$ .

$\frac{7 \cdot 49}{49 x^{3}} - \frac{9 x \cdot x^{3}}{49 x^{3}}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 49 - 9 x \cdot x^{3}}{49 x^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $49$ .

$\frac{343 - 9 x \cdot x^{3}}{49 x^{3}}$

Step 6.2

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

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Step 6.2.1

Move $x^{3}$ .

$\frac{343 - 9 (x^{3} x)}{49 x^{3}}$

Step 6.2.2

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

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Step 6.2.2.1

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

$\frac{343 - 9 (x^{3} x^{1})}{49 x^{3}}$

Step 6.2.2.2

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

$\frac{343 - 9 x^{3 + 1}}{49 x^{3}}$

Step 6.2.3

Add $3$ and $1$ .

$\frac{343 - 9 x^{4}}{49 x^{3}}$