Yoga has been around for thousands of years. The most well-known yogic scriptures like the Bhagavad Gita and Yoga Sutras of Patanjali explain yoga as a path to enlightenment, an ability to access the higher mind. This is achieved mostly through meditation, the physical practice of yoga (asana) has only been around for the past couple of hundred years. The use of asana was only used to get the body prepared for stillness during meditation.
My take on all of the above is that yoga is a form of moving meditation. If meditation is clearing of the mind then power yoga certainly does this for me as it involves deep concentration on the postures and attention to my ujjayi breath. However, the actual act of daily meditation is still extremely valuable. I love guided meditations, but the real magic happens when I sit in silence and observe the activity of my mind. This is called Pratyahara, one of the 8 limbs of yoga taught by Patanjali in the Yoga Sutras.