Question

What is 1.08 to the power of
`(1)/(5)`? Show your steps

Answer 1

Explanation:

`a^(1)/(n)=\sqrt[n]{a}\\\\1.08^(1)/(5)=\sqrt[5]{1.08}\qquad\text{convert the decimal to the fraction}\\\\=\sqrt[5]{(108)/(100)}=\sqrt[5]{(108\cdot1000)/(100\cdot1000)}=\sqrt[5]{(108000)/(100000)}=\frac{\sqrt[5]{108000}}{\sqrt[5]{100000}}=\frac{\sqrt[5]{108000}}{10}\\\\\text{You can use a calculator:}\\\\1.08^(1)/(5)=\sqrt[5]{1.08}\approx1.015511`

Answer 2

1.01551

Explanation:

1.08^1/5 = 1.01551

There's really no way of showing work for this problem unless you wanna convert 1/5 to a decimal and multiply that way.

I just did it on the calculator because most schools allow you to do exponents this way.