Question

HELP! How would I find the correct simplification
8^2 x 8^-5

Answer 1

\[8^{2} * 8 ^{-5}\]
both have exponents, so you have to check Laws of exponents
\[a ^{m} * a ^{n} = a ^{m + n}\]
can you see both have the same base = 8
now lets do as the Law says:
\[8^{2 - 5}\]
\[= 8^{-3}\]
Another Law of exponents:
\[a ^{-m} = \frac{ 1 }{ a ^{m} }\]
you can see that our base of 8 has a negative number so lets lets apply our law.
\[\frac{ 1 }{ 8^{3} }\] or \[\frac{ 1 }{ 512 }\]



hope this helps