1.2.4.2 Simplify an expression using only positive indices

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Name	Status	Author	Last Modified
1.2.4.2 Simplify an expression using only positive indices	Ready to use	Merryn Horrocks	28/06/2023 05:34
1.2.4 Task: Simplify an expression using only positive indices	Ready to use	Merryn Horrocks	08/07/2023 06:46

Question statement

Simplify $\displaystyle{\var{q2_expr}}$ . Do not use any negative indices in your answer.

Give any introductory information the student needs.

			Name	Type	Generated Value

alphabet	list	List of 20 items
q2_letter	integer	14
q2_expr	expression	14^(-6)*14^9/14^9
q2_ans	expression	1/14^6
q2_idx	integer	-6
q2_negidx	integer	6
q2_idx1	integer	-6
q2_idx2	integer	9
q2_idx3	integer	9
v	expression	14

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','v','w','x','y','z']

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `list`

[ "a", "b", "c", "d", "f", "g", "h", "k", "m", "n", "p", "q", "r", "s", "t", "v", "w", "x", "y", "z" ]

→ Used by:

q2_letter

This variable doesn't seem to be used anywhere.

Advice

First simplify the numerator using the first law of indices.

$\var{q2_expr}=\frac{\var{v}^{(\var{q2_idx1})+(\var{q2_idx2})}}{\var{v}^{(\var{q2_idx3})}}=\frac{\var{v}^{(\var{q2_idx1+q2_idx2})}}{\var{v}^{(\var{q2_idx3})}}$

Then use the second law.

$=\var{v}^{(\var{q2_idx1+q2_idx2})-(\var{q2_idx3})}=\var{v}^{\var{q2_idx1+q2_idx2-q2_idx3}}$

$=1$

$=\var{v}$

Finally, convert to a positive index.

$=\frac{1}{\var{v}^{\var{-1*(q2_idx1+q2_idx2-q2_idx3)}}}$

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This question is used in the following exams:

HELM Book 1.2 Mastery by Merryn Horrocks in HELM books.
HELM Book 1.2 Diagnostic by Merryn Horrocks in HELM books.
HELM Book 1.2 Indices by Merryn Horrocks in HELM books.
HELM Book 1.2.4 exercises by Merryn Horrocks in HELM books.

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1.2.4.2 Simplify an expression using only positive indices

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Merryn Horrocks 1 year, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

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Generated value: `list`

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1.2.4.2 Simplify an expression using only positive indices

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Merryn Horrocks 2 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`