Mathematics
OpenStudy (anonymous):

use rational expression to write (see comments for work) as a single radical expression

OpenStudy (anonymous):

$\sqrt[4]{2}\times \sqrt[3]{5}$

OpenStudy (mertsj):

Just remember that in a fractional (rational) exponent the top number is the power and the bottom number is the root. so: $\sqrt[4]{2}=2^{\frac{1}{4}}$

OpenStudy (mertsj):

Now you do the third root of 5

OpenStudy (anonymous):

the options are $\sqrt[12]{10} , \sqrt[12]{10000000} , \sqrt[12]{5000}, 1/5000^{12}$

OpenStudy (mertsj):

The third one.

OpenStudy (mertsj):

$2^{\frac{1}{4}}(5^{\frac{1}{3}})=x$ $\log2^{\frac{1}{4}}(5^{\frac{1}{3}})=\log x$ $\log 2^{\frac{1}{4}}+\log 5^{\frac{1}{3}}=logx$ $\frac{1}{4}\log2 + \frac{1}{3}\log5 = \log x$ $\frac{3}{12}\log2 + \frac{4}{12} \log 5 = \log x$ $\frac{1}{12}(3\log 2 + 4 \log 5 ) = \log x$ $\frac{1}{12}(\log 2^3 + \log 5^4)=\log x$ $\frac{1}{12}(\log 8 + \log 625)=\log x$ $\frac{1}{12} \log 5000=\log x$ $\log 5000^{\frac{1}{12}}=\log x$ $5000^{\frac{1}{12}}=x$ $\sqrt[12]{5000}=x$