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Sloane Stephens has heard a lot of advice from Serena Williams. Pointers on her groundstrokes, and even on her grunts.

It's been mostly gentle encouragement, occasionally spiced with headline-making comments from Williams, who has predicted the 19-year-old American will one day top the women's rankings.

As Stephens learned earlier this month, though, it's one thing to play with Williams, another to play against the 15-time Grand Slam champion.

When they meet Wednesday at the Australian Open, Williams will have the experience of 34 previous Grand Slam quarterfinals behind her. With a comeback 6-1, 3-6, 7-5 win over Bojana Jovanovski, Stephens qualified for her first quarterfinal at a major tournament.

"It will be tough, obviously. It's quarters of a Grand Slam," Stephens said. "There won't be that, like, first time, 'Oh, my God, I'm playing Serena.' That's kind of out of the window now. So that's good."

Williams and defending champion Victoria Azarenka advanced Monday, losing just four games between them against Russian rivals. Williams beat No. 14 Maria Kirilenko 6-2, 6-0, and Azarenka defeated Elena Vesnina 6-1, 6-1.

Next up for Azarenka is a quarterfinal against Svetlana Kuznetsova, who entered the season's first major tournament ranked No. 75 but has won titles at the 2004 U.S. Open and 2009 French Open.

On the men's side, No. 2 Roger Federer and U.S. Open champion Andy Murray stayed on course for a semifinal in their half of the draw.

Federer won 6-4, 7-6 (4), 6-2 over big-serving Canadian Milos Raonic, advancing to the quarterfinals at a Grand Slam for the 35th consecutive time, while Murray took advantage of Gilles Simon's fatigue for a 6-3, 6-1, 6-3 victory.

Federer will face 2008 Australian finalist Jo-Wilfried Tsonga, who beat friend and fellow Frenchman Richard Gasquet 6-4, 3-6, 6-3, 6-2.

Murray, who ended a 76-year drought for British men in Grand Slam tournaments with a win at the U.S. Open, will next play unseeded Frenchman Jeremy Chardy.

Chardy, who hit with Williams in a training camp at Mauritius at the end of 2012, followed up his upset win over 2009 U.S. Open champion Juan Martin del Potro with a 5-7, 6-3, 6-2, 6-2 victory over No. 21 Andreas Seppi.

Top-ranked Novak Djokovic, who needed five hours to beat Stanislas Warwinka in the fourth round, is on the other side of the draw. He'll face No. 5 seed Tomas Berdych on Tuesday.

Williams played Stephens at the Brisbane International earlier this month, winning their quarterfinal 6-4, 6-3 en route to the title. That night, Stephens said, she "lost to the best player in the world."

But there were times in the match when the American teenager was cranky, particularly when Williams unleashed some loud and long "Come ons" to celebrate vital points.

Stephens, looking toward her coach at one point, said the celebrations were disrespectful.

Later, she said she was just joking.

Regardless, it was a lesson. The friendly Serena from the locker room is the ultimate competitor — she's on a 20-match winning roll and has lost only once since her first-round exit at the French Open.

"Obviously every match is a learning experience," Stephens said. "But, I mean, you've just got to go and treat it like another match."

Well, not exactly a normal match, she said, but certainly no different from playing any of the other top three players.

"It just happens to be Serena. She's obviously one of the greatest players to ever play the game," Stephens said. "Without the titles, with the titles, it's still a tennis match. The court's the same size. You're still playing a regular person across the net."

Stephens and Williams ran across each other in the locker room Sunday.

"She told me I was too quiet on the court," Stephens said. "Then today I was thinking to myself, 'I'm really loud. Should I tone it down a little bit?'"

Stephen's mother, Sybil Smith, will be watching on television. Her grandparents are avid TV fans, too. Her father, former New England Patriots player John Stephens, died in 2009.

It was her mom who introduced her to tennis at age 9. About four years ago, Williams spotted her in the dressing room and said hi.

Last year, she practiced with Williams in Fed Cup training. And last week, she was even mistaken for the five-time Australian Open champion.

"Nothing is worse than on the second point of the match, someone screaming out, 'Serena!' I'm like, 'Oh, great, here we go.' That happened first match, like loudly," she said.

Williams thinks she's more like an elder stateswoman for the younger U.S. players than mentor for the likes of Stephens.

"I just feel like being the older one ... maybe some of the younger players look up to me," she said. "It's hard to be a real mentor when you're still in competition."

And as the elder stateswoman, Williams said, "I feel no responsibility" when it comes to playing Stephens.

"I doubt she has any expectations of me to be responsible for anything," she said. "I'm here to compete and do the best I can, as well as she is. And she's been doing really amazing. I'm really happy. I have a tough match, so we'll see."

As for the advice on the grunt, Williams said a little bit of locker room banter goes a long way.

"We were the other day in the locker room. She said, 'I grunt.' I said, 'No, you don't. You're so calm. I'm like loud and outrageous,'" Williams recalled.

"She's incredibly calm. I think that's such a great thing to have. Like you look at some of the great players like Roger, he's so calm out there. That's what she has. She's like, 'I grunt.' I'm like, 'You don't grunt. What are you talking about?' I think she was maybe joking, because she definitely doesn't grunt."