FIND THE MISSING BASE OF AN EXPONENT

To find the missing base of an exponent, we need to follow the steps given below.

Step 1 :

First we have to factor the number which does not have exponent.  

Step 2 :

According to the exponent of the missing base, we can regroup the factors on the side of the equation. 

Step 3 :

Once we get the same exponent on both sides, we can equate the bases and find the missing base. 

Practice Problems

Problem 1 :

Write the missing base

Solution :

Let "x" be the missing base

To find the value missing base, we have to split 1000 as much as possible.

On both sides we have same powers, so they must have same base.

So, the missing base is 10.

Problem 2 :

Write the missing base

Solution :

Let "x" be the missing base

To find the value missing base, we have to split 256 as much as possible.

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Now we have to split this as four groups.  So each group will contain 4.

On both sides we have same powers, so they must have same base.

So, the missing base is 4.

Problem 3 :

Write the missing base

Solution :

Let "x" be the missing base

To find the value missing base, we have to split 9 and 16 as much as possible.

9  =  3 x 3  =  3²

16  =  4 x 4  =  4²

(9/16)  =  (3/4)²

 (3/4)²  =  x²

On both sides we have same powers, so they must have same base.

So, the missing base is 3/4.

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