Question

How do I compare taking a root and raising to a power?

Answer 1

Raising a power indicates that you are multiplying the number by itself 'n' times when you raise the power to n.

Eg: Suppose there are 2 boys having 2 pairs of shirts each. How many shirts in total?

Lets do it manually first, there are 2 boys. Each boy is having 2 pairs of shirts. 1 Pair of shirts means 2.

Total number of shirts here, boy1 = 2 pairs = 2x2 =4 = 2²

boy 2 = 2 pairs = 2x2 =4 = 2²

Total shirts = bo1 shirts + boy2 shirts = 4+4 =8 = 2³

Using Power, we could have done it directly = 2boysx2 pairs = 2x2x2 = 2³= 8

Now taking a root is inverse to the raising a power.

If we raise a power by 2 and taking a square root, you will get the same number.

If we raise a power by 3 and taking a cube root, you will get the same number.

Basically these two are inverse operations by comparison.

Hope it helps!