Question

Which equation is equivalent to 16 Superscript 2 p Baseline = 32 Superscript p + 3?
8 Superscript 4 p Baseline = 8 Superscript 4 p + 3
8 Superscript 4 p Baseline = 8 Superscript 4 p + 12
2 Superscript 8 p Baseline = 2 Superscript 5 p + 15
2 Superscript 8 p Baseline = 2 Superscript 5 p + 3

Answer 1

Rewrite with base 2: 16 = 2^4 and 32 = 2^5. So

16^{2p} = (2^4)^{2p} = 2^{8p},
32^{p+3} = (2^5)^{p+3} = 2^{5p+15}.

Thus the equivalent equation is 2^{8p} = 2^{5p+15} (the third choice).