smc

When we multiply numbers with exponents, we add the exponents together and leave the bases unchanged. We can apply this concept to computate $256^{0.16}\cdot 256^{0.09}$: $$256^{0.16}\cdot 256^{0.09}=256^{0.16+0.09}=256^{0.25}.$$ Now we can convert the decimal exponent to a fraction: $$256^{0.25}=256^{\frac{1}{4}}.$$ Now, let us convert the expression into radical form. Since $4$ is the denominator of the fractional exponent, it will be the index exponent: $$256^{\frac{1}{4}}=\sqrt[4]{256}.$$ Since $256=16^2=(4^2{)}^2=4^4$, we can solve for the fourth root of $256$: $$\sqrt[4]{256}=\sqrt[4]{4^4}=4.$$ Therefore, $(256{)}^{.16}\cdot (256{)}^{.09}=\boxed{4}.$