Question

I have been stuck on these for a while. Any help is greatly appreciated? Please answer all parts and explain.

Answer 1

Key Concepts

• Exponent rules

Solution

Anything raised to a negative power is equal its reciprocal raised to a positive power.

`a^(-m)=(1)/(a^m)`

Therefore, we can raise any number, as long as they are not equal to 0 or 1, to a negative integer exponent to represent fractions between 0 and 1.

Fractional exponents represent a radical.

`a^{(m)/(n)}=\sqrt[n]{a^m}`

Knowing this, we can simplify the given number:

`(3^(1/5))^2\\=(\sqrt[5]{3})^2\\=\sqrt[5]{3^2}\\=\sqrt[5]{9}`