Laws of Indices

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From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Lauren Richards	said	Has some problems	7 years, 8 months ago
Elliott Fletcher	said	Needs to be tested	7 years, 9 months ago
Aiden McCall	said	Has some problems	7 years, 9 months ago

From users who are not members of Transition to university :

Anne Else

said

Ready to use

5 years, 9 months ago

History

○

Anne Else 5 years, 9 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 5 years, 10 months ago

Saved a checkpoint:

Replaced string restrictions and javascript with pattern restrictions.

Restore this checkpoint

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

It looks like parts e and f had some constant coefficients in the advice which weren't present in the actual question, so I've removed those.

Otherwise, this looks good!

Restore this checkpoint

○

Lauren Richards 7 years, 8 months ago

Gave some feedback: Has some problems

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Lauren Richards commented 7 years, 8 months ago

I would scrap the first sentence of the statement. It should be in the description. I think I would just write "Using the laws of indices, simplify each expression down to its simplest form." The bit that you have afterwards that states "Recall that a^0=1..." didn't apply to any of the questions I was given, and it seems to be a random place to have this bit of info.

In part c), you suggested that the user could use the rule a^-m=1/a^m but when I tried to write my answer in that form it did not accept it. I wouldn't suggest you suggest to the user to use the second rule.

Typo in part b) of the advice - explicity instead of explicitly.

I'm not sure, but I don't know if the advice for the alternative method of part c) is correct or clear enough. I thought that that rule was a way of reorganising the fraction rather than actually calculating stuff and that if you used it, the final answer of (8a^4)/(3a^6) would be 8/(3a^2) not 8/3(a^-2). I may well be wrong hahaha so just ignore me if so!

I think you're missing a \displaystyle in part e) of the advice.

I think the bit you have written at the end of part e) "This can be simplified further if possible." is a bit random. I would scrap it.

I think you're missing some displaystyles in part f) of the advice as well.

I think generally the question is very good and the advice is very clear and concise!

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Aiden McCall 7 years, 9 months ago

Gave some feedback: Has some problems

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Aiden McCall commented 7 years, 9 months ago

Advice:
For all parts, not 100% sure on this but personally I would omit the commas after each line of the equation and just have some punctuation at the end such as a full stop or comma like you have done, just not every line.
a) Very good
b) To read easier I would remove 'Then' from the first line and 'that' from the second. Also possibly but 'Therefore' (the one before the equation) on another line.
All other parts were good just the commas in the equations.

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher commented 7 years, 9 months ago

Scratch that

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Has some problems

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Elliott Fletcher commented 7 years, 9 months ago

Thanks for the feedback Aiden, think i should have fixed all of the string restrictions now.

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Aiden McCall 7 years, 9 months ago

Gave some feedback: Has some problems

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Aiden McCall commented 7 years, 9 months ago

a) Inputting the question gives the correct answer this can be fixed by restricting the string *

b) As above

c) Restrict strings ( )

d) As above

e) and f) are good. Rest of the question is good just the string parts.

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 9 months ago

This mainly looks good.

Try to avoid long runs of maths in-line with text - they're quite hard to read. Put long bits of maths in display mode, and don't be afraid to use lots of paragraph breaks.

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Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Elliott Fletcher 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Elliott Fletcher 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Laws of Indices	Ready to use	Elliott Fletcher	01/04/2020 09:09
Katherine's copy of Laws of Indices	draft	Katherine Tomlinson	01/08/2017 12:15
Eva's copy of Laws of Indices	draft	Eva Szatmari	12/06/2018 15:50
Laws of Indices [L6] Randomised	Doesn't work	Matthew James Sykes	25/07/2018 10:28
1. Laws of indices	draft	emma rand	27/07/2018 13:08
Ed's copy of Laws of Indices	draft	Ed Southwood	08/08/2022 10:18
Simon's copy of Laws of Indices	draft	Simon Thomas	04/03/2019 13:47
Blathnaid's copy of Simon's copy of Laws of Indices	draft	Blathnaid Sheridan	04/11/2019 13:00
David's copy of Laws of Indices	draft	David Goulding	11/03/2019 17:43
John's copy of Laws of Indices	draft	John Wick	17/06/2019 10:01
J. Richard's copy of Laws of Indices	draft	J. Richard Snape	15/08/2019 17:17
J. Richard's copy of Laws of Indices	draft	J. Richard Snape	15/08/2019 17:19
rekenregels van machten	draft	Johan Maertens	20/08/2019 16:36
Laws of Indeces 2	draft	Leonardo Juliano	07/10/2019 09:50
Ugur's copy of Laws of Indices	Ready to use	Ugur Efem	08/11/2021 16:45

There are 90 other versions that do you not have access to.

Question statement

Using the laws of indices, simplify each expression down to its simplest form. Recall that $a^{0} = 1$ for any number $a$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	6
y	integer	4
c	integer	4
d	integer	5
p	integer	9
q	integer	5
b	integer	9
g	integer	8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9 except y)

JME function reference

Description

Used in parts a,c and e

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part c)" - prompt
"Part c)" → "Unnamed gap" - Correct answer

Parts

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Part d) Gap-fill
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Part e) Gap-fill
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Part f) Gap-fill
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Write $a^{\var{x}} \times a^{\var{y}}$ as a single power of $a$ .

$a^{\var{x}} \times a^{\var{y}} =$ Unnamed gap.

Advice

a)

Here we are using the rule of indices: $a^m \times a^n = a^{m+n}$ .

Using this rule,

$\begin{align} a^\var{x} \times a^\var{y}\ &= a^\simplify[all, !collectNumbers]{{x}+{y}}\\ &= a^\var{x+y}. \end{align}$

b)

We are asked to find $\var{c}a^\var{p} \times \var{d}a^\var{q}$ .

Notice there is a constant in front of each of the terms.

To do this, write the product out explicitly, as

$\var{c}a^\var{p} \times \var{d}a^\var{q} = \var{c} \times \var{d} \times a^\var{p} \times a^\var{q}.$

We know that $\var{c} \times \var{d} = \var{c*d}$ , and using the rule of indices: $a^\var{p} \times a^\var{q} = a^\var{p+q}$ .

Therefore:

$\begin{align} \var{c}a^\var{p} \times \var{d}a^\var{q}&= \var{c*d} \times a^\var{p+q} \\ &= \simplify{{c*d}*a^{p+q}}. \end{align}$

c)

Here we are using: $a^m \div a^n = a^{m-n}$ .

We are asked to simplify the expression, $\displaystyle\simplify{{b}*a^{x}/({g}*a^{y})}$ .

To do this, we just have to use the previously mentioned rule of indices. We write this out explicity as

$\simplify{{b}*a^{x}/({g}*a^{y})} = \simplify{{b}/{g}} \times \simplify{a^{x}/(a^{y})}.$

Using rules of indices,

$\begin{align} \frac{a^\var{x}}{a^\var{y}} &= a^\var{x} \div a^\var{y}\\ &= a^\simplify[all, !collectNumbers]{{x}-{y}}\\ &= a^\var{x-y}. \end{align}$

Therefore,

$\begin{align} \frac{\var{b}a^\var{x}}{\var{g}a^\var{y}} &= \simplify{{b}/{g}} \times \simplify{a^{{x}-{y}}}\\ &= \simplify{{b}/{g}*a^{x-y}}. \end{align}$

Alternatively,

Using the rule of indices: $a^{-m} = \displaystyle\frac{1}{a^{m}}$ , we can rewrite the question as:

$\begin{align} \frac{\var{b}a^\var{x}}{\var{g}a^\var{y}} &= \simplify{{b}/{g}} \times \frac{a^\var{x}}{a^\var{y}}\\ &= \simplify{{b}/{g}} \times a^\var{x} \times a^{-\var{y}}. \end{align}$

And then using the rule: $a^m \times a^n = a^{m+n}$ , this becomes:

$\begin{align} \simplify{{b}/{g}} \times a^\var{x} \times a^{-\var{y}} &= \simplify{{b}/{g}} \times a^\simplify[all,!collectNumbers]{{x}+(-{y})}\\ &= \simplify{{b}/{g}*a^{x-y}}. \end{align}$

d)

The question asks us to simplify $(\simplify{{c}*a^{p}})^{\var{q}}$ .

To do this we use the rules:

$(a^{m})^{n} = a^{mn},$

$(ab)^m = a^mb^m.$

We can then expand the equation as

$(\simplify{{c}*a^{p}})^{\var{q}}= \var{c}^{\var{q}} \times (a^{\var{p}})^{\var{q}}.$

Then using the rule of indices mentioned previously,

$\begin{align} (\simplify{{c}*a^{p}})^{\var{q}}&= \simplify{{c}^{q}} \times a^\var{p*q}\\ &= \simplify{{c}^{q}*a^{p*q}}. \end{align}$

e)

The question asks us to simplify $\sqrt[\var{d}]{\var{x}^\var{d}a}$ .

To do this we use the rules:

$a^\frac{1}{m} = \sqrt[m]{a},$

$(ab)^m = a^mb^m.$

We can expand the expression as follows:

$\begin{align} \sqrt[\var{d}]{a} &= (\simplify{a})^\frac{1}{\var{d}}\\ &= a^\frac{1}{\var{d}}. \end{align}$

f)

The question requires us to simplify $\sqrt[\var{c}]{a^\var{q}}$ .

Here, we use the rule of indices: $a^\frac{n}{m} = \sqrt[m]{a^n}$ , allowing us to expand the expression as follows:

$\begin{align} \sqrt[\var{c}]{\simplify{a^{q}}} &= \simplify[fractionnumbers,all]{(a^{q})^{{1}/{{c}}}}\\ &= \simplify[fractionnumbers,all]{a^{{q}/{c}}}. \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Anne Else 5 years, 9 months ago

Christian Lawson-Perfect 5 years, 10 months ago

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Elliott Fletcher 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Aiden McCall commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Elliott Fletcher commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Elliott Fletcher commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Aiden McCall commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Elliott Fletcher 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

Generated value: `integer`