The 5th power of n is 16

Question

What is it in numbers?

Answer 1

Let's solve this problem using algebra.

• n to the power of 5 is 16 : (original problem)
• n^5 = 16 : (problem restated as an equation)
• (n^5)^0.2 = 16^0.2 : (take both sides to the power of 0.2 - because 0.2 is the inverse of 5, i.e. 1/0.2 = 5)
• n^(5*0.2) = 16^0.2 : (restating the powers)
• n^1 = 16^0.2 : (multiplying 5*0.2)
• n = 16^0.2 : (a number to the power of one is just the same number)
• n = 1.7411011 : (solve for 16^0.2)

 

We can check our answer using a calculator. If you put 1.7411011 into a calculator and take it to the fifth power (or 1.7411011^5), you'll get 16.

 

This site has more useful information regarding powers:

 

http://lasp.colorado.edu/~bagenal/MATH/math61.html