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Q. If \( 16^{2x+3} = 64^{x+3} \), find \( 4^{2x-2} \)
(a) 64 (b) 256 (c) 32 (d) 512
✏️ Solution
\( 16 = 2^4,\quad 64 = 2^6 \)
\( (2^4)^{2x+3} = (2^6)^{x+3} \)
\( 2^{8x+12} = 2^{6x+18} \)
\( 8x + 12 = 6x + 18 \Rightarrow x = 3 \)
\( 4^{2x-2} = 4^{6-2} = 4^4 \)
\( = 256 \)
Correct Option: (b) 256
\( \boxed{256} \)