Indices: Simplification 3a

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Created this as a copy of Indices: Simplification 2b.

Name	Status	Author	Last Modified
Surds: Simplifying Expressions 1a	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 1b	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 2b	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 2a	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 3a	Ready to use	Ben McGovern	15/08/2023 15:31
Surds: Simplifying Expressions 3b	Ready to use	Ben McGovern	15/08/2023 15:14
Surds: Simplifying Expressions 4a	Ready to use	Ben McGovern	15/08/2023 15:29
Surds: Simplifying Expressions 4b	Ready to use	Ben McGovern	15/08/2023 15:26
Surds: Simplifying Expressions 4c	Ready to use	Ben McGovern	15/08/2023 15:50
Surds: Simplifying Expressions 5a - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 15:55
Surds: Simplifying Expressions 5b - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 16:07
Surds: Simplifying Expressions 6 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Surds: Simplifying Expressions 7 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Quadratics: Using the Quadratic Formula	Ready to use	Ben McGovern	14/09/2022 16:14
Quadratics: Factorisation 1	Ready to use	Ben McGovern	14/08/2023 15:01
Quadratics: Factorisation 2	Ready to use	Ben McGovern	14/08/2023 15:14
Quadratics: Completing the Square 1	Ready to use	Ben McGovern	14/08/2023 14:59
Quadratics: Completing the Square 2	Ready to use	Ben McGovern	14/09/2022 16:03
Quadratics: Interpreting the Discriminant	Ready to use	Ben McGovern	14/09/2022 16:08
Quadratics: Factorisation 3 - Difference of 2 squares	Ready to use	Ben McGovern	14/08/2023 15:33
Indices: Simplification 1a	Ready to use	Ben McGovern	26/06/2023 12:12
Indices: Simplification 1b	Ready to use	Ben McGovern	26/06/2023 14:31
Indices: Simplification 1c	Ready to use	Ben McGovern	26/06/2023 14:30
Indices: Simplification 2a	Ready to use	Ben McGovern	26/06/2023 14:33
Indices: Simplification 2b	Ready to use	Ben McGovern	26/06/2023 14:36
Indices: Simplification 3a	Ready to use	Ben McGovern	26/06/2023 14:37
Indices: Simplification 3b	Ready to use	Ben McGovern	26/06/2023 14:40
Indices: Change of Notation 1	Ready to use	Ben McGovern	15/08/2023 11:43
Indices: Change of Notation 2	Ready to use	Ben McGovern	15/08/2023 11:51
Indices: Change of Notation 3	Ready to use	Ben McGovern	15/08/2023 11:54
Solve Quadratics - Factorisation 1	Ready to use	Ruth Hand	14/08/2023 15:44
Quadratics: Solving a Quadratic Equation	Ready to use	Ben McGovern	09/12/2022 16:45
Quadratics: Solving by Factorisation	Ready to use	Ben McGovern	14/09/2022 16:25
AD2 Quadratics - solve	Ready to use	Megan Oliver	09/04/2024 15:13
AD5 Difference of two squares	Ready to use	Megan Oliver	09/04/2024 15:14
AA2 Indices - divide	Ready to use	Andrew Neate	09/04/2024 15:00
AA4 Indices - Fractional 2	Ready to use	Andrew Neate	09/04/2024 15:01
AA3 Indices - Fractional 1	Ready to use	Andrew Neate	09/04/2024 15:01
AA1 Indices - times	Ready to use	Andrew Neate	28/03/2024 13:17
Calculation with indices - times	Ready to use	Will Morgan	26/06/2024 11:53
Calculation with Indices - divide	Ready to use	Will Morgan	26/06/2024 12:07

There are 209 other versions that do you not have access to.

Question statement

Without a calculator, simplify the following expression into a single integer:

$\var{a}^3 \times \var{a^4}^{1/2}$

Give any introductory information the student needs.

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Advice

To simplify $\var{a}^3 \times \var{a^4}^{1/2}$ , we want to make use of the following 2 rules:

$\left(a^n\right)^m =a^{n\times m}$ ;
$a^n \times a^m = a^{n+m}$ .

Notice that we can rewrite this expression so that both numbers are in terms of $\var{a}$ , since $\var{a^4} = \var{a}^4$ :

$\var{a}^3 \times \var{a^4}^{1/2} = \var{a}^3 \times \left(\var{a}^4\right)^{1/2}.$

Applying rule 1 to the second term:

$\begin{split} \var{a}^3 \times \left(\var{a}^4\right)^{1/2} &\,= \var{a}^3 \times \var{a}^{4 \times 1/2} \\ &\,= \var{a}^3 \times \var{a}^2. \end{split}$

Then applying rule 2:

$\var{a}^3 \times \var{a}^2 = \var{a}^5.$

Therefore,

$\begin{split} \var{a}^3 \times \var{a^4}^{1/2} &\,= \var{a}^5 \\ &\,= \var{a^5}. \end{split}$

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This question is used in the following exams:

Algebra DIAGNOSYS trial by Ruth Hand in Ruth's workspace.
Indices by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Indices by Ben McGovern in MASH Bath: Moodle quizzes and TS.
All the good stuff by Chris Templet in Chris's workspace.
ASSIGNMENT DUE 21ST JULY 2023 AT 11:53:13 by Martin Jarvis in Martin's workspace.
New Exam by Ben Tito in Ben's workspace.
Testing of the website by Manpreet Singh in Manpreet's workspace.
Test 1 - unrelated topics by Emma Coutts in SQA Higher Diagnostic Test.
Test 2 - inter-related topics by Emma Coutts in SQA Higher Diagnostic Test.
Indices 2 by Luke Middleton in Luke's workspace.

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Ben McGovern 2 years, 6 months ago

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Ben McGovern 4 years, 8 months ago

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Indices: Simplification 3a

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`