Pre-Algebra Examples

$7 x^{- 2} - 33^{- 1} + 20$

Step 1

Write $7 x^{- 2} - 33^{- 1} + 20$ as an equation.

$y = 7 x^{- 2} - 33^{- 1} + 20$

Step 2

Simplify $7 x^{- 2} - 33^{- 1} + 20$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$y = 7 \frac{1}{x^{2}} - 33^{- 1} + 20$

Step 2.1.2

Combine $7$ and $\frac{1}{x^{2}}$ .

$y = \frac{7}{x^{2}} - 33^{- 1} + 20$

Step 2.1.3

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

$y = \frac{7}{x^{2}} - \frac{1}{33} + 20$

Step 2.2

To write $20$ as a fraction with a common denominator, multiply by $\frac{33}{33}$ .

$y = \frac{7}{x^{2}} - \frac{1}{33} + 20 \cdot \frac{33}{33}$

Step 2.3

Combine $20$ and $\frac{33}{33}$ .

$y = \frac{7}{x^{2}} - \frac{1}{33} + \frac{20 \cdot 33}{33}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{7}{x^{2}} + \frac{- 1 + 20 \cdot 33}{33}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $20$ by $33$ .

$y = \frac{7}{x^{2}} + \frac{- 1 + 660}{33}$

Step 2.5.2

Add $- 1$ and $660$ .

$y = \frac{7}{x^{2}} + \frac{659}{33}$

Step 3

The given equation $y = \frac{7}{x^{2}} + \frac{659}{33}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$