Question

Can Someone Help Me W/ This -Giving Medals-

Answer 1

here is the pic

Answer 2

\[2^{M} = 1/8\]

Answer 3

this rules will help you,
\[u^v=e^{v \times \ln u}\]
\[\ln({e^x})=x\]
\[\ln(1/a)=-\ln(a)\]

Answer 4

one idea to try (and for these questions, it probably always works)
is to see if you can multiply the base (the 2 in this problem)
times itself, and get the number 8

2*2*2= 8
that means you can write it as \(2^3\) using the "short-hand way" (with exponents)

\[ 2^m= \frac{1}{2^3} \]
that looks promising , except the right side is "upside-down"
you can "flip" the fraction *if you make the exponent negative*
in other words
\[ \frac{1}{2^3} = \frac{2^{-3}}{1} = 2^{-3} \]

so now it is
\[ 2^m = 2^{-3} \]
now pattern match... what should m be to make both sides look the same ?