To show that [tex]y = b^{x+h} = ab^x[/tex], first use the property that a sum in an exponent can be written as product of bases with the separate parts as their exponents:
[tex]b^{x+h} = b^x\cdot b^h[/tex]
from that, it is easy to see that, if x varies, but h does not, [tex]b^h[/tex] is constant and can be written as a number, say, "a", so
[tex]y=b^{x+h} = b^x\cdot b^h=a\cdot b^x[/tex]
which completes the algebraic argument.
