Question

How do I rewrite the rational exponent as a radical by extending the properties of integer exponents.?

Answer 1

\(\Large \bf a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad

\sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}\)

Answer 2

2 7/8
-----
2 1/4

It gives me that and im still unsure how to do it..?

Answer 3

\(\Large \bf { a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}}
\\ \quad \\ \quad \\

\cfrac{2^{\frac{{\color{blue}{ 7}}}{{\color{red}{ 8}}}}}{2^{\frac{{\color{blue}{ 1}}}{{\color{red}{ 4}}}}} }\)

so... what do you think?

Answer 4

hmmm lemme rewrite that a bit because it may need it

Answer 5

You'd make it \[\sqrt[8]{2^{7}}\] and \[\sqrt[4]{2^{1}}\] right?

Answer 6

well. that is correct

Answer 7

however...lemme do a quick rewrite like \(\bf \Large { a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}}\qquad \qquad \cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}}\implies a^{-\frac{{\color{blue} n}}{{\color{red} m}}}
\\ \quad \\ \quad \\


\cfrac{2^{\frac{{\color{blue}{ 7}}}{{\color{red}{ 8}}}}}
{
2^{\frac{{\color{blue}{ 1}}}{{\color{red}{ 4}}}}
}\implies

\cfrac{2^{\frac{{\color{blue}{ 7}}}{{\color{red}{ 8}}}}}{1}\cdot \cfrac{1}{2^{\frac{{\color{blue}{ 1}}}{{\color{red}{ 4}}}}}\implies

2^{\frac{{\color{blue}{ 7}}}{{\color{red}{ 8}}}}\cdot 2^{-\frac{{\color{blue}{ 1}}}{{\color{red}{ 4}}}}\implies 2^{\frac{{\color{blue}{ 7}}}{{\color{red}{ 8}}}-\frac{{\color{blue}{ 1}}}{{\color{red}{ 4}}}} }\)

Answer 8

The first way was much easier in my heab lol im Dyslexic so im kinda harder to teach

Answer 9

ohh hmm maybe you're not meant to simplify that much
just to change it to radical notation then :), so that's ok

Answer 10

It gives me 4 choices
\[\sqrt[8]{2^{5}}\]
\[\sqrt[5]{2^{8}}\]
\[\sqrt{2} \frac{ 5 }{ 8 }\]
\[\sqrt[4]{2}^{6}\]

That's why im kinda confused because I thought it'd be
\[\sqrt[8]{2^{7}} and \sqrt[4]{2}^{1}\]