Powers and Roots Practice Test 3

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Question : 39 of 40

Marks: +1, -0

The value of

[{(1.331)^{-1}+(1.33)^{-2}+...+(1.331)^{-7}}/{(1.33)^{-2}+(1.331)^{-3}+...+(1.331)^{-8}}]^{2/3}

is equal to:

$(1.331)^{-2}$
$1.331$
$(1.1)^{-2}$
$1.21$

Solution:

[{(1.331)^{-1}+(1.331)^{-2}+...+(1.331)^{-7}}/{(1.331)^{-2}+(1.331)^{-3}+...+(1.331)^{-8}}]^{2/3}

=[(1.331)^{-1}/(1.331)^{-2} × {1+(1.331)^{-1}+...+(1.331)^{-6}}/{1+(1.331)^{-1}+...+(1.331)^{-6}}]^{2/3}

=[(1.331)^{-1}/(1.331)^{-2}]^{2/3}

=[(1.331)^{2}/(1.331) ]^{2/3}=(1.331)^{2/3}

=√^3{(1.1×1.1×1.1)^2}

=1.1×1.1=1.21

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