Algebra Examples

$(7.5 x \cdot 10^{- 5}) + (1.3 x \cdot 10^{- 5})$

Step 1

Simplify each term.

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Step 1.1

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

$7.5 x \cdot \frac{1}{10^{5}} + 1.3 x \cdot 10^{- 5}$

Step 1.2

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

$7.5 x \cdot \frac{1}{100000} + 1.3 x \cdot 10^{- 5}$

Step 1.3

Multiply $7.5 x \frac{1}{100000}$ .

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Step 1.3.1

Combine $7.5$ and $\frac{1}{100000}$ .

$x \frac{7.5}{100000} + 1.3 x \cdot 10^{- 5}$

Step 1.3.2

Combine $x$ and $\frac{7.5}{100000}$ .

$\frac{x \cdot 7.5}{100000} + 1.3 x \cdot 10^{- 5}$

Step 1.4

Move $7.5$ to the left of $x$ .

$\frac{7.5 \cdot x}{100000} + 1.3 x \cdot 10^{- 5}$

Step 1.5

Factor $7.5$ out of $7.5 \cdot x$ .

$\frac{7.5 (x)}{100000} + 1.3 x \cdot 10^{- 5}$

Step 1.6

Factor $100000$ out of $100000$ .

$\frac{7.5 (x)}{100000 (1)} + 1.3 x \cdot 10^{- 5}$

Step 1.7

Separate fractions.

$\frac{7.5}{100000} \cdot \frac{x}{1} + 1.3 x \cdot 10^{- 5}$

Step 1.8

Divide $7.5$ by $100000$ .

$0.000075 \frac{x}{1} + 1.3 x \cdot 10^{- 5}$

Step 1.9

Divide $x$ by $1$ .

$0.000075 x + 1.3 x \cdot 10^{- 5}$

Step 1.10

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

$0.000075 x + 1.3 x \cdot \frac{1}{10^{5}}$

Step 1.11

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

$0.000075 x + 1.3 x \cdot \frac{1}{100000}$

Step 1.12

Multiply $1.3 x \frac{1}{100000}$ .

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Step 1.12.1

Combine $1.3$ and $\frac{1}{100000}$ .

$0.000075 x + x \frac{1.3}{100000}$

Step 1.12.2

Combine $x$ and $\frac{1.3}{100000}$ .

$0.000075 x + \frac{x \cdot 1.3}{100000}$

Step 1.13

Move $1.3$ to the left of $x$ .

$0.000075 x + \frac{1.3 \cdot x}{100000}$

Step 1.14

Factor $1.3$ out of $1.3 \cdot x$ .

$0.000075 x + \frac{1.3 (x)}{100000}$

Step 1.15

Factor $100000$ out of $100000$ .

$0.000075 x + \frac{1.3 (x)}{100000 (1)}$

Step 1.16

Separate fractions.

$0.000075 x + \frac{1.3}{100000} \cdot \frac{x}{1}$

Step 1.17

Divide $1.3$ by $100000$ .

$0.000075 x + 0.000013 \frac{x}{1}$

Step 1.18

Divide $x$ by $1$ .

$0.000075 x + 0.000013 x$

Step 2

Add $0.000075 x$ and $0.000013 x$ .

$0.000088 x$