Jinhua's copy of Indices 2

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Deactivated user 8 years, 6 months ago

Created this as a copy of Indices 2.

Name	Status	Author	Last Modified
Indices 1	Ready to use	joshua boddy	01/06/2016 09:47
Indices 2	Ready to use	joshua boddy	01/06/2016 09:47
Numerical Skills Indices 1 - Formative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Indices 2 - Formative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Indices 1 - Summative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Indices 2 - Formative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Indices 2 - Summative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Algebra IV: Properties of indices (2) - Fractions	Ready to use	Sarah Turner	05/08/2016 14:06
Algebra IV: Properties of indices (3) - Negative integers/fractions	Ready to use	Sarah Turner	07/08/2016 10:38
Algebra IV: Properties of indices (3) - Negative integers/fractions	Ready to use	Nasir Firoz Khan	12/08/2016 16:11
Algebra IV: Properties of indices (2) - Fractions	Ready to use	Nasir Firoz Khan	12/08/2016 16:10
Jinhua's copy of Indices 1	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Indices 2	draft	Jinhua Mathias	28/08/2024 12:15
Simon's copy of Algebra IV: Properties of indices (2) - Fractions	draft	Simon Thomas	04/03/2019 12:34
Maria's copy of Algebra IV: Properties of indices (2) - Fractions	draft	Maria Aneiros	30/05/2019 04:05

There are 6 other versions that do you not have access to.

Question statement

Simplify the following and find their final values (either in integer or fraction form).

Note: Look out for the fractions in either the base or the index which may be simplified before proceeding to evaluate. If you're unsure with the method involved, click 'Reveal answers' and study the Advice section. Once you feel comfortable with the theory, click 'Try another question like this one' to regenerate the exercises.

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			Name	Type	Generated Value

a	integer	3
b	integer	4
c	number	16
d	number	27
f	integer	4
g	integer	2
h	number	9
j	integer	5
k	integer	3
l	number	32
f1	integer	4
f2	integer	3
f3	number	125
f4	number	625
t1	number	8
t2	number	27

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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)

Negative indices are used in the same way as positive indices, except that the index is applied to the reciprocal of the base. That is, the fraction which represents the base value is flipped upside-down.

In this case, $\var{c}$ , which is represented by the fraction $\frac{\var{c}}{1}$ , is raised to the power of $\simplify{1/-{b}}$ . This can be simplified in the following way:

$\frac{\var{c}}{1}^\simplify{1/-{b}}=\frac{\var{1}}{\var{c}}^\simplify{1/{b}}$

You can then follow the more familiar process of evaluating positive powers:

$\frac{1}{\var{c}}^\simplify{1/{b}}=\frac{1}{{\var{c}}^\simplify{1/{b}}}$ $=\frac{1}{2}$

Part f)

In this case, the base is already presented in fraction form. Usingthe steps decribed above, it can be simplified as follows:

$\left(\simplify{3/11}\right)^{-2}=\left(\simplify{11/3}\right)^{2}=\left(\frac{11^2}{3^2}\right)=\left(\frac{\simplify{11^2}}{\simplify{3^2}}\right)$

Part g)

$\left(\simplify{1/{f4}}\right)^{\simplify{-{f2}/{f1}}}=\left(\frac{\var{f4}}{1}\right)^{\simplify{{f2}/{f1}}}=\var{f4}^{\simplify{{f2}/{f1}}}=\simplify{{f4}^{{f2}/{f1}}}$

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Jinhua's copy of Indices 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Deactivated user 8 years, 6 months ago

Error in variable testing condition

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Generated value: integer

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Number entry

Advanced settings

Generated value: `integer`