Index Laws 3

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

Express the following in the form $2^{\alpha} 3^{\beta}$ , writing the $\alpha$ and $\beta$ in the boxes provided. Write the powers as fractions or as integers.

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	1
b	integer	2
d	integer	5
g	integer	3
f	integer	4
h	integer	3
k	integer	4
j	integer	3
m	integer	1
l	integer	2
t1	integer	4
a1	integer	4
t	integer	4
m3	integer	-30
m2	integer	61
n2	integer	12
n	integer	2
b1	integer	4

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Name

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Value

xxxxxxxxxx
 
random(0..4 except b)

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Description

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Generated value: `integer`

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Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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Gap-fill

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${\LARGE\sqrt[\var{t1}]{\var{2^{a1}*3^{b1}}}}$

$\alpha =$ Gap 0., $\beta =$ Gap 1.

Advice

Write each of the numbers as a power of 2 multiplied by a power of 3, write the n'th root as: to the power 1/n. Then apply the index laws to combine the powers. Thus

${\LARGE\sqrt[\var{t1}]{\var{2^{a1}*3^{b1}}}=(2^{\var{a1}}*3^{\var{b1}})^{1/\var{t1}}=(2^{\var{a1}})^{1/\var{t1}}*(3^{\var{b1}})^{1/\var{t1}}=2^{\simplify{{a1}/{t1}}} 3^{\simplify{{b1}/{t1}}}},$

${\LARGE\dfrac{(\var{2^b * 3^c})^{\var{d}}*(\var{2^f * 3^g})^{1/\var{h}}}{(\var{2^j *3^k})^{\var{l}}*\sqrt[\var{t}]{\var{2^m *3^n}}}=\dfrac{(2^{\var{b}} * 3^{\var{c}})^{\var{d}}*(2^{\var{f}} * 3^{\var{g}})^{1/\var{h}}}{(2^{\var{j}} *3^{\var{k}})^{\var{l}}*(2^{\var{m}} *3^{\var{n}})^{1/\var{t}}}}$

${\LARGE =\dfrac{(2^{\var{b*d}} * 3^{\var{c*d}})*(2^{\var{f}/\var{h}} * 3^{\var{g}/\var{h}})}{(2^{\var{j*l}} *3^{\var{k*l}})*(2^{\var{m}/\var{t}} *3^{\var{n}/\var{t}})} =\dfrac{2^{\var{b*d}} * 3^{\var{c*d}}*2^{\var{f}/\var{h}} * 3^{\var{g}/\var{h}}}{2^{\var{j*l}} *3^{\var{k*l}}*2^{\var{m}/\var{t}} *3^{\var{n}/\var{t}}}}$

${\LARGE =2^{\var{b*d}} *2^{\var{f}/\var{h}}*2^{\var{-j*l}}*2^{-\var{m}/\var{t}} * 3^{\var{c*d}} * 3^{\var{g}/\var{h}} *3^{-\var{k*l}}*3^{-\var{n}/\var{t}} =2^{\simplify{{m2}/{n2}}} 3^{\simplify{{m3}/{n2}}}}$

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Taxonomy: mathcentre

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Index Laws 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`