which equation is equivalent to $16^{2p}=32^{p + 3}$?\n$8^{4p}=8^{4p+3}$\n$8^{4p}=8^{4p + 12}$\n$2^{8p}=2^{5p…

which equation is equivalent to $16^{2p}=32^{p + 3}$?\n$8^{4p}=8^{4p+3}$\n$8^{4p}=8^{4p + 12}$\n$2^{8p}=2^{5p+15}$\n$2^{8p}=2^{5p+3}$

which equation is equivalent to $16^{2p}=32^{p + 3}$?\n$8^{4p}=8^{4p+3}$\n$8^{4p}=8^{4p + 12}$\n$2^{8p}=2^{5p+15}$\n$2^{8p}=2^{5p+3}$

Answer

Explanation:

Step1: Rewrite bases as powers of 2

Since $16 = 2^4$ and $32=2^5$, we rewrite the given equation $16^{2p}=32^{p + 3}$. $(2^4)^{2p}=(2^5)^{p + 3}$

Step2: Apply power - of - a - power rule

The power - of - a - power rule $(a^m)^n=a^{mn}$. For the left - hand side, $(2^4)^{2p}=2^{4\times2p}=2^{8p}$. For the right - hand side, $(2^5)^{p + 3}=2^{5\times(p + 3)}=2^{5p+15}$. So the equivalent equation is $2^{8p}=2^{5p + 15}$.

Answer:

$2^{8p}=2^{5p + 15}$