Index Laws 4

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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 $x^{\alpha} y^{\beta}$ , 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	3
b	integer	1
d	integer	3
g	integer	1
f	integer	4
h	integer	3
k	integer	4
j	integer	2
l	integer	4
t1	integer	5
a1	integer	1
b1	integer	3
m3	integer	-20
m2	integer	-11

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Value

xxxxxxxxxx
 
random(1..4 except b)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

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This variable doesn't seem to be used anywhere.

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
  Add
2. Gap Gap 1. Mathematical expression
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Gap-fill

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${\LARGE\sqrt[\var{t1}]{x^{\var{a1}}*y^{\var{b1}}}}$

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

Advice

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

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

${\LARGE\dfrac{(x^{\var{b}} * y^{\var{c}})^{\var{d}}*(x^{\var{f}} * y^{\var{g}})^{1/\var{h}}}{(x^{\var{j}} *y^{\var{k}})^{\var{l}}} =\dfrac{(x^{\var{b*d}} * y^{\var{c*d}})*(x^{\var{f}/\var{h}} * y^{\var{g}/\var{h}})}{(x^{\var{j*l}} *y^{\var{k*l}})} }$

${\LARGE =x^{\var{b*d}} *x^{\var{f}/\var{h}}*x^{\var{-j*l}} * y^{\var{c*d}} * y^{\var{g}/\var{h}} *y^{-\var{k*l}} =x^{\simplify{{m2}/{h}}} y^{\simplify{{m3}/{h}}}}$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

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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 4

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`