Index Laws 2

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

Express the following as a power of a, writing the power in the box provided. Write the power as a fraction or as an integer.

Give any introductory information the student needs.

			Name	Type	Generated Value

f2	integer	4
h2	integer	-1
t2	integer	2
b2	integer	2
n	integer	12
d2	integer	-2
q2	integer	1
s2	integer	4
m2	integer	4
a	integer	3
g2	integer	3
a1	integer	3
a2	integer	4
c2	integer	-1
p2	integer	4
c	integer	-1
b	integer	3
d	integer	5
f	integer	4
m	integer	-39
t1	integer	3
t	integer	3
n2	integer	8

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Name

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Value

xxxxxxxxxx
 
random(2..5 except [b,0])

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Description

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Generated value: `integer`

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Advice
"Part c)" - prompt

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

${\LARGE\sqrt[\var{t1}]{a^\var{a1}}}$

The power is Unnamed gap

Advice

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

${\LARGE\sqrt[\var{t1}]{a^\var{a1}}=(a^\var{a1})^{1/\var{t1}}=a^{\simplify{{a1}/{t1}}}},$

${\LARGE\dfrac{\sqrt[\var{t}]{a^\var{a}}*(a^\var{b})^{\var{c}}}{(a^\var{d})^{1/\var{f}}}=\dfrac{(a^{\var{a}})^{1/ \var{t}} * (a^{\var{b}})^{\var{c}}}{(a^{\var{d}})^{1/\var{f}}}=\dfrac{a^{\var{a}/\var{t}} * a^{\var{b* c}}}{a^{\var{d}/\var{f}}}}$

${\LARGE=a^{\var{a}/\var{t}} * a^{\var{b* c}}*a^{-\var{d}/\var{f}}=a^{\simplify{{m}/{n}}}},$

${\LARGE\dfrac{\sqrt[\var{s2}]{a^{\var{b2}}*(a^{\var{c2}})^{\var{d2}}}}{\sqrt[\var{t2}]{a^{\var{f2}}*(a^{\var{g2}})^{\var{h2}}}}=\dfrac{(a^{\var{b2}}*a^{\var{c2*d2}})^{1/\var{s2}}}{(a^{\var{f2}}*a^{\var{g2*h2}})^{1/\var{t2}}}}$

${\LARGE=\dfrac{(a^{\var{b2+c2*d2}})^{1/\var{s2}}}{(a^{\var{f2+g2*h2}})^{1/\var{t2}}}=\dfrac{a^{\simplify{{p2}/{s2}}}}{a^{\simplify{{q2}/{t2}}}}=a^{\simplify{{m2}/{n2}}}}$

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Natalia Martsinovich 2 years, 5 months ago

Newcastle University Mathematics and Statistics 9 years, 2 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 2

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Taxonomy: mathcentre

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Contributors

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History

Comment

Checkpoint description

Natalia Martsinovich 2 years, 5 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`