If 32 raised to the 2 c power is equal to 8 raised to the c plus 7 power , what is the value of c ?

Rewrite both bases as powers of 2: 32 = 2^5 and 8 = 2^3. Then (2^5)^(2c) = (2^3)^(c+7), so the exponents are 10c and 3c + 21. Equating them gives 10c = 3c + 21, so c = 3; the correct choice is 3.

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