に応えて— In Response To / Living Up To

• ファンの期待に応えて、彼は見事に優勝した。

  Fan no kitai ni kotaete, kare wa migoto ni yuushou shita.

  Living up to his fans' expectations, he won the championship splendidly.

  期待に応えて = acting so as to satisfy the fans' expectations.

• 住民の要望に応えて、新しい公園が作られた。

  Juumin no youbou ni kotaete, atarashii kouen ga tsukurareta.

  In response to residents' requests, a new park was built.

  要望に応えて shows the action taken to meet the residents' demands.

• みんなの声援に応える走りを見せたい。

  Minna no seien ni kotaeru hashiri wo misetai.

  I want to run in a way that lives up to everyone's cheers.

  に応える modifies 走り, meaning a performance worthy of the support.

• ・Typically pairs with 期待, 要望, 要求, 声援, 願い.
• ・Register: formal to neutral; common in news and speeches.
• ・Note the kanji 応える (to respond) — distinct from 答える (to answer a question).

Commonly confused with

The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones に応えて is tested against.

• ～も～ば～も — Both This And That
• ～ことは～が — True, But…
• ～つつ — While / Even Though
• ～というと／といえば／といったら — Speaking Of
• にかかわらず — Regardless Of / Irrespective Of
• にせよ〜にせよ — Whichever the Case
• にもかかわらず — In Spite of It All
• ～のみならず — Not Only, But Also