Algebra IV: Properties of indices (1) - Multiplication/Division

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Sarah Turner

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John Hodkinson 8 years, 7 months ago

Gave some feedback: Ready to use

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Sarah Turner 8 years, 7 months ago

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Sarah Turner 8 years, 7 months ago

Created this as a copy of Indices 3.

Name	Status	Author	Last Modified
Indices 3	Ready to use	joshua boddy	01/06/2016 09:47
Numerical Skills Indices 3 - Formative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Indices 3 - Summative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Algebra IV: Properties of indices (1) - Multiplication/Division	Ready to use	Sarah Turner	19/08/2016 14:22
Algebra IV: Properties of indices (1) - Multiplication/Division	Ready to use	Nasir Firoz Khan	12/08/2016 16:11
Rachel's copy of Algebra IV: Properties of indices (1) - Multiplication/Division	Ready to use	Rachel Staddon	09/05/2018 06:54
Jinhua's copy of Indices 3	Ready to use	Jinhua Mathias	28/08/2024 12:15
2. Laws of indices	draft	emma rand	27/07/2018 13:09
Simon's copy of Algebra IV: Properties of indices (1) - Multiplication/Division	draft	Simon Thomas	04/03/2019 12:23
Simon's copy of Algebra IV: Properties of indices (1) - Multiplication/Division	draft	Simon Thomas	04/03/2019 12:33
Maria's copy of Algebra IV: Properties of indices (1) - Multiplication/Division	draft	Maria Aneiros	30/05/2019 04:04
Indices - Multiplication/Division	draft	Kevin Bohan	26/09/2019 09:14
Indices - Multiplication/Division 2	draft	Kevin Bohan	26/09/2019 10:25
Ugur's copy of Indices - Multiplication/Division	Ready to use	Ugur Efem	01/11/2021 12:31

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Question statement

Simplify each of the following expressions, giving your answer in its simplest form.

Click 'Show steps' for guidance on which index law is applicable.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	8
c	integer	0
d	integer	-2
f	integer	2
g	integer	3
h	integer	2
j	integer	3

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Generated value: `integer`

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Recall the laws of indices to help solve the problems:

$x^a \times x^b = x^{a+b}$

$x^a \div x^b = x^{a-b}$

$x^{-a} = \frac{1}{x^a}$

$(x^a)^b = x^{ab}$

$(\frac{x}{y})^a = \frac{x^a}{y^a}$

$x^\frac{a}{b} = (\sqrt[b]{x})^{a}$

$x^0 = 1$

Worked Solutions:

Part a) $x^{(\var{a}+\var{b})}=\simplify{x^{({a}+{b})}}$

Part b) $p^{(\var{c}+\var{d})}=\simplify{p^{({c}+{d})}}$

Part c) $\var{a}^\var{f}\times{k^{(\var{b}\times\var{f})}}=\simplify{{a}^{f}*k^{({b}*{f})}}$

Part d) $y^{((\var{a}+\var{b})/(\var{a}\times\var{b}))}=y^{\frac{\simplify{{a}+{b}}}{\simplify{{a}*{b}}}}$

Part e) $c^{(\var{a}-\var{b})}=c^\simplify{({a}-{b})}$

Part f) $\frac{\var{a}}{\var{b}}h^{\var{c}-\var{d}}=\frac{\var{a}}{\var{b}}{\simplify{h^{{c}-{d}}}}$

Part g) $\frac{4^\var{g}}{2^\var{h}}\times{d^{\var{g}-\var{h}}}=\simplify{(4^{g})/(2^{h})*d^{g-h}}$

Part h) $\frac{6^\var{g}}{9^\var{h}}\times{p^{\var{h}\var{j}-\var{g}\var{f}}}=\simplify{(6^{g})/(9^{h})*p^{h*j-g*f}}$

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Algebra IV: Properties of indices (1) - Multiplication/Division

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John Hodkinson 8 years, 7 months ago

Sarah Turner 8 years, 7 months ago

Sarah Turner 8 years, 7 months ago

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Algebra IV: Properties of indices (1) - Multiplication/Division

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

John Hodkinson 8 years, 7 months ago

Sarah Turner 8 years, 7 months ago

Sarah Turner 8 years, 7 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`