AA4 Indices - Fractional 2 - Numbas at mathcentre.ac.uk

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From users who are members of Skills Audits for Maths and Stats :

Lauren Desoysa	said	Ready to use	1 year ago
Andrew Neate	said	Needs to be tested	1 year, 1 month ago

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Will Morgan 11 months, 2 weeks ago

Published this.

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Lauren Desoysa 1 year ago

Gave some feedback: Ready to use

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Andrew Neate 1 year, 1 month ago

Gave some feedback: Needs to be tested

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Andrew Neate 1 year, 1 month ago

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

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

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Question statement

Evaluate the following expression:

$\var{a^n}^{\frac{\var{m}}{\var{n}}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

m	integer	2
n	integer	3
a	integer	4

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xxxxxxxxxx
 
random(2,3)

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Generated value: `integer`

→ Used by:

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Advice

To find $\var{a^n}^{\frac{\var{m}}{\var{n}}}$ , we want to make use of the following rule:

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

By rewriting the power $\frac{\var{m}}{\var{n}}$ as a product of $\var{m} \times \frac{1}{\var{n}}$ , we can apply this rule:

$\begin{split} \var{a^n}^{\frac{\var{m}}{\var{n}}} &\,= \var{a^n}^{\left(\var{m} \times \frac{1}{\var{n}}\right)} \\ &\,= \left(\var{a^n}^\frac{1}{\var{n}}\right)^\var{m} \\ &\,= \var{a}^\var{m}\end{split}$

Then calculating what is left:

$\begin{split} \var{a}^\var{m} &\,=\var{a^(m)} \end{split}$

Therefore,

$\var{a^n}^{\frac{\var{m}}{\var{n}}} =\var{a^(m)}.$

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AA4 Indices - Fractional 2

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Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Number entry

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AA4 Indices - Fractional 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year ago

Andrew Neate 1 year, 1 month ago

Andrew Neate 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`