1.3 Powers - Revision history

Phil: Idiomatic English, localisation of terminology and notation

2008-12-30T15:14:29Z

Idiomatic English, localisation of terminology and notation

Jdinglis at 13:57, 26 October 2008

2008-10-26T13:57:47Z

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-	'''Keep in mind that:'''	+	'''Keep in mind that...'''

	The number raised to the power 0 is always 1 as long as the number (the base) is not 0.		The number raised to the power 0 is always 1 as long as the number (the base) is not 0.

Eakc07: Minor Grammatical changes

2008-10-22T00:00:27Z

Minor Grammatical changes

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	<ol type="a">		<ol type="a">
-	<li><math>\quad 3^{5/6} > 3^{3/4}\quad</math> as the base <math>3</math> is greater than <math>1</math> and the first exponent <math>5/6</math> is greater than the second exponent <math>3/4</math>.</li>	+	<li><math>\quad 3^{5/6} > 3^{3/4}\quad</math> because the base <math>3</math> is greater than <math>1</math> and the first exponent <math>5/6</math> is greater than the second exponent <math>3/4</math>.</li>
	<li><math>\quad 3^{-3/4} > 3^{-5/6}\quad</math> as the base is greater than <math>1</math> and the exponents satisfy <math> -3/4 > - 5/6</math>.</li>		<li><math>\quad 3^{-3/4} > 3^{-5/6}\quad</math> as the base is greater than <math>1</math> and the exponents satisfy <math> -3/4 > - 5/6</math>.</li>
-	<li><math> \quad 0{,}3^5 < 0{,}3^4 \quad</math>as the base <math> 0{,}3</math> is between <math>0</math> and <math>1</math> and <math>5 > 4</math>.	+	<li><math> \quad 0\text{.}3^5 < 0\text{.}3^4 \quad</math>as the base <math> 0\text{.}3</math> is between <math>0</math> and <math>1</math> and <math>5 > 4</math>.
	</ol>		</ol>
	</div>		</div>

-	If a power has a positive exponent, it increases as the base increases. The opposite applies if the exponent is negative, that is the power decreases as the base increases.	+	If a power has a positive exponent it increases as the base increases. The opposite applies if the exponent is negative, that is to say the power decreases as the base increases.

	<div class="exempel">		<div class="exempel">
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	</div>		</div>

-	Sometimes powers need to be rewritten in order to determine the relative sizes. For example to compare <math>125^2</math> with <math>36^3</math>~~one~~ can rewrite them as	+	Sometimes powers need to be rewritten in order to determine the relative sizes. For example to compare <math>125^2</math> with <math>36^3</math> we can rewrite them as
	{{Displayed math\|\|<math>		{{Displayed math\|\|<math>
	125^2 = (5^3)^2 = 5^6\quad \text{and}\quad 36^3 = (6^2)^3 = 6^6		125^2 = (5^3)^2 = 5^6\quad \text{and}\quad 36^3 = (6^2)^3 = 6^6
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	''' Example 11'''		''' Example 11'''

-	Determine which of the following pairs of numbers is the greater	+	Determine which of the following pairs of numbers is the greater:

	<ol type="a">		<ol type="a">
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	The base 25 can be rewritten in terms of the second base <math>5</math> by putting <math>25= 5\cdot 5= 5^2</math>. Therefore		The base 25 can be rewritten in terms of the second base <math>5</math> by putting <math>25= 5\cdot 5= 5^2</math>. Therefore

-	{{Displayed math\|\|<math>25^{1/3} = (5^2)^{1/3} = 5^{2 \cdot \frac{1}{3}}= 5^{2/3}</math>}}	+	{{Displayed math\|\|<math>25^{1/3} = (5^2)^{1/3} = 5^{2 \cdot \frac{1}{3}}= 5^{2/3}\text{,}</math>}}

-	~~and then~~ we see that	+	hence we see that

	{{Displayed math\|\|<math>5^{3/4} > 25^{1/3} </math>}}		{{Displayed math\|\|<math>5^{3/4} > 25^{1/3} </math>}}
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	{{Displayed math\|\|<math>\eqalign{8 &= 2\cdot 4 = 2 \cdot 2 \cdot 2 = 2^3\mbox{,}\\ 128 &= 2\cdot 64 = 2\cdot 2\cdot 32 = 2\cdot 2\cdot 2\cdot 16 = 2\cdot 2\cdot 2\cdot 2\cdot 8\\ &= 2\cdot 2\cdot 2\cdot 2\cdot 2^3 = 2^7\mbox{.}}</math>}}		{{Displayed math\|\|<math>\eqalign{8 &= 2\cdot 4 = 2 \cdot 2 \cdot 2 = 2^3\mbox{,}\\ 128 &= 2\cdot 64 = 2\cdot 2\cdot 32 = 2\cdot 2\cdot 2\cdot 16 = 2\cdot 2\cdot 2\cdot 2\cdot 8\\ &= 2\cdot 2\cdot 2\cdot 2\cdot 2^3 = 2^7\mbox{.}}</math>}}

-	This ~~means that~~	+	This gives

	{{Displayed math\|\|<math>\begin{align*}		{{Displayed math\|\|<math>\begin{align*}
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	<br>		<br>
	<br>		<br>
-	Since <math>8=2^3</math> and <math>27=3^3</math> a first step ~~can be~~ to simplify and write the numbers as powers of <math>2</math> and <math>3</math> respectively,	+	Since <math>8=2^3</math> and <math>27=3^3</math>, the first step is to simplify and write the numbers as powers of <math>2</math> and <math>3</math> respectively,

	{{Displayed math\|\|<math>\begin{align*}		{{Displayed math\|\|<math>\begin{align*}
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	<br>		<br>
	<br>		<br>
-	We rewrite the exponents ~~so they have~~ a common denominator	+	We rewrite the exponents due to them having a common denominator

	{{Displayed math\|\|<math>\frac{1}{3} = \frac{2}{6} \quad</math> and <math>\quad \frac{1}{2} = \frac{3}{6}</math>.}}		{{Displayed math\|\|<math>\frac{1}{3} = \frac{2}{6} \quad</math> and <math>\quad \frac{1}{2} = \frac{3}{6}</math>.}}

-	~~Then we have that~~	+	This gives

	{{Displayed math\|\|<math>\begin{align*}		{{Displayed math\|\|<math>\begin{align*}
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	'''Keep in mind that:'''		'''Keep in mind that:'''

-	The number raised to the power 0, is always 1~~, if~~ the number (the base) is not 0.	+	The number raised to the power 0 is always 1 as long as the number (the base) is not 0.

Eakc07: Minor grammatical changes

2008-10-21T23:37:07Z

Minor grammatical changes

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Tekbot: Robot: Automated text replacement (-{{Fristående formel +{{Displayed math)

2008-09-10T13:54:09Z

Robot: Automated text replacement (-{{Fristående formel +{{Displayed math)

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Robot: Automated text replacement (-{{Vald flik +{{Selected tab)

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Tekbot: Robot: Automated text replacement (-1.3 Potenser +1.3 Powers)

2008-09-10T13:12:26Z

Robot: Automated text replacement (-1.3 Potenser +1.3 Powers)

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Tekbot: Robot: Automated text replacement (-Övningar +Exercises)

2008-09-10T10:37:41Z

Robot: Automated text replacement (-Övningar +Exercises)

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2008-09-09T12:18:53Z

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