Question

write the expression 243^-4/5 radical notation and then evaluate the radical notation

Answer 1

SO when you have a fraction for an exponent, the top denominator tells you what root it is and the numerator tells you the power of the number inside of the root. So since this is 4/5, it will be a number to the 4th power and then to the 5th root. Now since this is a negative exponent, that means in order to make it positive, you move it into the denominator. For example:

\[2^{-2} = \frac{ 1 }{ 2^{2} }\]
An example of the fraction exponent
\[3^{\frac{ 3 }{ 7 }} = \sqrt[7]{3^{3}}\]

Answer 2

So with those examples, think you might be able to do it?

Answer 3

Follow what @Psymon wrote, but notice that sometimes is't easier to first take the root and then raise the number to the power.

\(\large{a^{\frac{ m }{ n }} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^m }\)

Example:

\(\large{64^{\frac{ 5 }{ 6 }} = \sqrt[6]{64^{5}} = (\sqrt[6]{64})^5 =( 2)^5 = 32}\)

Answer 4

For solving, it's usually easier to take the root, lol. But in terms of explanation of the set up I just put it in the order Idid.