Question

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

Answer 1

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

Answer 2

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

Answer 3

Now you do the third root of 5

Answer 4

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

Answer 5

The third one.

Answer 6

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