Question

Simplify cube root of 5 over fourth root of 5.

5 to the power of 1 over 4

5 to the power of 1 over 12

5 to the power of 7 over 12

5 to the power of 4 over 3

Answer 1

@jdoe0001

Answer 2

\(\bf \Large \sqrt[3]{\cfrac{5}{5}}\quad ?\)

Answer 3

hmmm ohhh over fourth... so

Answer 4

yeah

Answer 5

you mean \(\Large \bf \cfrac{\sqrt[3]{5}}{\sqrt[4]{5}}\quad ?\)

Answer 6

yes

Answer 7

hmmm do you know how to add fractions?

Answer 8

yes

Answer 9

one sec

Answer 10

\(\large \bf {\sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}
\\ \quad \\ \quad \\
\cfrac{\sqrt[3]{5}}{\sqrt[4]{5}}\implies\cfrac{\sqrt[3]{5^1}}{\sqrt[4]{5^1}}\implies \cfrac{5^{\frac{1}{3}}}{5^{\frac{1}{4}}}
\implies \cfrac{5^{\frac{1}{3}}}{1}\cdot \cfrac{1}{5^{\frac{1}{4}}}
\\ \quad \\
\cfrac{1}{a^{-\color{red} n}}\implies \cfrac{1}{\frac{1}{a^{\color{red} n}}}\implies a^{{\color{red} n}}\qquad thus
\\ \quad \\
\cfrac{5^{\frac{1}{3}}}{1}\cdot \cfrac{1}{5^{\frac{1}{4}}}\implies \cfrac{5^{\frac{1}{3}}}{1}\cdot 5^{{\color{blue}{ -}}\frac{1}{4}}\implies 5^{\frac{1}{3}}\cdot 5^{{\color{blue}{ -}}\frac{1}{4}}
\\ \quad \\
5^{\frac{1}{3}{\color{blue}{ -}}\frac{1}{4}}
}\)

Answer 11

hmm anyhow, I used the mistaken.... I meant to say -> \(\large \bf \cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}= \cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}}\implies a^{-\frac{{\color{blue} n}}{{\color{red} m}}}\)