Jinhua's copy of Indices 3

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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

There are 27 other versions that do you not have access to.

Question statement

Simplify each of these, giving your answer in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

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

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Name

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Value

xxxxxxxxxx
 
random(2..9)

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Generated value: `integer`

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Advice

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)

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

Part b)

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

Part c)

For this question, recall that the exterior power is applied to both the coefficient and the variable within brackets.

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

Part d)

$y^{\simplify{1/{a}}} \times y^{\simplify{1/{b}}}=y^{\frac{1}{\var{a}}+\frac{1}{\var{b}}}=y^{\simplify{{{a}+{b}}/{{a}*{b}}}}$

Part e)

$\frac{c^{\var{a}}}{c^{\var{b}}}=c^{\var{a}-\var{b}}=c^{\simplify{{a}-{b}}}$

Part f)

$\frac{\var{a}h^{\var{c}}}{\var{b}h^{\var{d}}}=\frac{\var{a}}{\var{b}}\times h^{\var{c}-\var{d}}=\simplify{{a}/{b}}h^{\simplify{{c}-{d}}}$

Part g)

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

Part h)

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

Give a worked solution to the whole question.

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This question is used in the following exams:

Indices and surds by Jinhua Mathias in Core Foundation Maths.
Indices and simultaneous equations by Jinhua Mathias in Maths 2.
Indices and simultaneous equations by Jinhua Mathias in Maths 2.

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Jinhua's copy of Indices 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jinhua Mathias 6 years, 5 months ago

Deactivated user 8 years, 6 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`