###### The problem

$(7x{10}^{x})+(7x{10}^{y})+(7x{10}^{z})=700070.07.Writedownapossiblesetofvaluesforx,yandz.(3marks).\phantom{\rule{0ex}{0ex}}$

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$(7x{10}^{x})+(7x{10}^{y})+(7x{10}^{z})=700070.07.Writedownapossiblesetofvaluesforx,yandz.(3marks).\phantom{\rule{0ex}{0ex}}$

$Solution:\phantom{\rule{0ex}{0ex}}Firstwritethenumberontherighthandside700070.07inexpandedform.\phantom{\rule{0ex}{0ex}}700070.07=700000+70+0.07\phantom{\rule{0ex}{0ex}}=7x{10}^{5}+7x{10}^{1}+7x{10}^{-2}(theaboveexpandedformins\mathrm{tan}dardform)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Nowcomparetheseexpandedformvalueswiththeequationgiveninquestion\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}7x{10}^{x}=7x{10}^{5}\Rightarrow x=5\phantom{\rule{0ex}{0ex}}7x{10}^{y}=7x{10}^{1}\Rightarrow y=1\phantom{\rule{0ex}{0ex}}7x{10}^{z}=7x{10}^{-2}\Rightarrow z=-2$