# How do you evaluate 10^(4log_10 2)?

Dec 20, 2016

${10}^{4 {\log}_{10} 2} = 16$

#### Explanation:

By definition of ${\log}_{10}$, for any $t > 0$ we have:

${10}^{{\log}_{10} t} = t$

Also note that for any $a , b$ we have:

${10}^{a b} = {\left({10}^{a}\right)}^{b}$

So:

${10}^{4 {\log}_{10} 2} = {\left({10}^{{\log}_{10} 2}\right)}^{4} = {2}^{4} = 16$