When simplified, what is the value of $$(10^{0.5})(10^{0.3})(10^{0.2})(10^{0.1})(10^{0.9})?$$
I notice that all the bases of the exponents are 10, so I can use the rule that says $$(a^b)(a^c) = a^{b+c}$$ for any base a. That means I can add up the exponents of 10 and get the same answer as multiplying the factors. The exponents are 0.5, 0.3, 0.2, 0.1, and 0.9. Adding them up, I get $$0.5 + 0.3 + 0.2 + 0.1 + 0.9 = 2$$ So the answer is the same as $$10^2 = 100$$ 