Pre-Algebra Examples

$5.17 x \cdot 10^{- 5} - 3.98 x \cdot 10^{- 4}$

Step 1

Write $5.17 x \cdot 10^{- 5} - 3.98 x \cdot 10^{- 4}$ as an equation.

$y = 5.17 x \cdot 10^{- 5} - 3.98 x \cdot 10^{- 4}$

Step 2

Simplify $5.17 x \cdot 10^{- 5} - 3.98 x \cdot 10^{- 4}$ .

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

$y = 5.17 x \cdot \frac{1}{10^{5}} - 3.98 x \cdot 10^{- 4}$

Step 2.1.2

Raise $10$ to the power of $5$ .

$y = 5.17 x \cdot \frac{1}{100000} - 3.98 x \cdot 10^{- 4}$

Step 2.1.3

Multiply $5.17 x \frac{1}{100000}$ .

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Step 2.1.3.1

Combine $5.17$ and $\frac{1}{100000}$ .

$y = x \frac{5.17}{100000} - 3.98 x \cdot 10^{- 4}$

Step 2.1.3.2

Combine $x$ and $\frac{5.17}{100000}$ .

$y = \frac{x \cdot 5.17}{100000} - 3.98 x \cdot 10^{- 4}$

Step 2.1.4

Move $5.17$ to the left of $x$ .

$y = \frac{5.17 \cdot x}{100000} - 3.98 x \cdot 10^{- 4}$

Step 2.1.5

Factor $5.17$ out of $5.17 \cdot x$ .

$y = \frac{5.17 (x)}{100000} - 3.98 x \cdot 10^{- 4}$

Step 2.1.6

Factor $100000$ out of $100000$ .

$y = \frac{5.17 (x)}{100000 (1)} - 3.98 x \cdot 10^{- 4}$

Step 2.1.7

Separate fractions.

$y = \frac{5.17}{100000} \cdot \frac{x}{1} - 3.98 x \cdot 10^{- 4}$

Step 2.1.8

Divide $5.17$ by $100000$ .

$y = 0.0000517 \frac{x}{1} - 3.98 x \cdot 10^{- 4}$

Step 2.1.9

Divide $x$ by $1$ .

$y = 0.0000517 x - 3.98 x \cdot 10^{- 4}$

Step 2.1.10

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

$y = 0.0000517 x - 3.98 x \cdot \frac{1}{10^{4}}$

Step 2.1.11

Raise $10$ to the power of $4$ .

$y = 0.0000517 x - 3.98 x \cdot \frac{1}{10000}$

Step 2.1.12

Multiply $- 3.98 x \frac{1}{10000}$ .

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Step 2.1.12.1

Combine $- 3.98$ and $\frac{1}{10000}$ .

$y = 0.0000517 x + x \frac{- 3.98}{10000}$

Step 2.1.12.2

Combine $x$ and $\frac{- 3.98}{10000}$ .

$y = 0.0000517 x + \frac{x \cdot - 3.98}{10000}$

Step 2.1.13

Move $- 3.98$ to the left of $x$ .

$y = 0.0000517 x + \frac{- 3.98 \cdot x}{10000}$

Step 2.1.14

Move the negative in front of the fraction.

$y = 0.0000517 x - \frac{3.98 \cdot x}{10000}$

Step 2.1.15

Factor $3.98$ out of $3.98 \cdot x$ .

$y = 0.0000517 x - \frac{3.98 (x)}{10000}$

Step 2.1.16

Factor $10000$ out of $10000$ .

$y = 0.0000517 x - \frac{3.98 (x)}{10000 (1)}$

Step 2.1.17

Separate fractions.

$y = 0.0000517 x - (\frac{3.98}{10000} \cdot \frac{x}{1})$

Step 2.1.18

Divide $3.98$ by $10000$ .

$y = 0.0000517 x - (0.000398 \frac{x}{1})$

Step 2.1.19

Divide $x$ by $1$ .

$y = 0.0000517 x - (0.000398 x)$

Step 2.1.20

Multiply $0.000398$ by $- 1$ .

$y = 0.0000517 x - 0.000398 x$

Step 2.2

Subtract $0.000398 x$ from $0.0000517 x$ .

$y = - 0.0003463 x$

Step 3

The given equation $y = - 0.0003463 x$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

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