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Just laws of exponents:
\[(f(x+h)-f(x))/h=(8^{x+h}-8^x)/h=(8^x 8^h-8^x)/h=8^x(8^h-1)/h\]

As i don't know the names of those laws I can't look up videos on them. Will you give me the names?

I don't understand what property/properties of exponents allow me to conclude 8^(x + h) = 8^x * 8^h

Yeah

We're applying this rule in reverse in this case.

k

That cleared things up, thanks.