People said she would be a 1 hit wonder with 'I Kissed A Girl,' yet she proved them wrong when both 'Hot N Cold' & 'Waking Up In Vegas' were top ten hits from One of the Boys.
After that, she released Teenage Dream which spurred 5 #1 singles, tying Michael Jackson's record. Lots of people were saying this was/would be her peak.
Yet she returned with PRISM. When 'Roar' came out and went #1 shortly after, people also said that it only was only successful because she was 'still riding off the success of Teenage Dream

' Unconditionally, despite it only being a holiday buzz single, still performed well, peaking at #14 on the Hot 100 respectively. Now shes back on top with 'Dark Horse.'
All of her albums have sold fairly well also. One of the Boys has sold 5,000,000+ WW, Teenage Dream 6,000,000+, and PRISM is a little over 2,250,000 right now. Teenage Dream and PRISM were also #1 albums in multiple countries around the world.
I should also mention that shes the most followed person on Twitter, with over 50.1 million followers. She also has over 63.4 million fans on Facebook. Clearly people aren't tired of or over her.
People continue to underestimate every move she makes, but ultimately she ends up with the last laugh.
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So, why do you think people keep underestimating her?