Question

What is 1.08 to the power of $\frac{1}{5}$? Show your steps

Answer 1

Answer:

1.01551

Step-by-step 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.

Answer 2

Step-by-step explanation:

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