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Exercises: Power Laws

Simplify the following terms.

$10 \cdot 10^{- 2} : 10^{4} + 10^{0}$

$x^{- 1} \cdot x^{2} \cdot x^{0} \cdot x^{- 3} \cdot x^{4}$

For this task you need the following basic knowledge: Power Laws
$x^{- 1} \cdot x^{2} \cdot x^{0} \cdot x^{- 3} \cdot x^{4}$ $=$
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Apply the power laws.
$=$ $x^{- 1 + 2 + 0 - 3 + 4}$
$=$ $x^{2}$
$10^{- 1} + 10^{- 2}$

For this task you need the following basic knowledge: Power Laws
$10^{- 1} + 10^{- 2}$ $=$
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Convert into fractions.
$=$ $\frac{1}{10} + \frac{1}{100}$
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Get both fractions to a common denominator.
$=$ $\frac{10}{100} + \frac{1}{100}$
$=$ $\frac{11}{100}$
$x^{- 1} + x^{- 2}$

For this task you need the following basic knowledge: Power Laws
$x^{- 1} + x^{- 2}$ $=$
↓
Apply the power laws.
$=$ $\frac{1}{x} + \frac{1}{x^{2}}$
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Get both fractions to a common denominator.
$=$ $\frac{x}{x^{2}} + \frac{1}{x^{2}}$
$=$ $\frac{1 + x}{x^{2}}$
$x^{- 2} - \frac{x^{2}}{x^{4}}$

For this task you need the following basic knowledge: Power Laws
$x^{- 2} - \frac{x^{2}}{x^{4}}$ $=$
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Apply the power laws.
$=$ $x^{- 2} - x^{2 - 4}$
$=$ $x^{- 2} - x^{- 2}$
$=$ $0$
$(\frac{1}{x} + x^{- 2}) \cdot 2 x$

For this task you need the following basic knowledge: Power Laws
$(\frac{1}{x} + x^{- 2}) \cdot 2 x$ $=$
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Write as fractions.
$=$ $(\frac{1}{x} + \frac{1}{x^{2}}) \cdot 2 x$
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Multiply out.
$=$ $\frac{2 x}{x} + \frac{2 x}{x^{2}}$
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You can still shorten these fractions.
$=$ $\frac{2 \cdot x}{x} + \frac{2 \cdot x}{x \cdot x}$
$=$ $2 + \frac{2}{x}$

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