# FIND THE MISSING BASE OF AN EXPONENT

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 is not having power as much as possible.

Step 2 :

According to the power of missing base, we can regroup the factors and put the power.

Step 3 :

On both sides, if the powers are equal then we can decide the bases are also equal.

Let us see the examples given below to understand the concept.

## Find the missing base of an exponent - Examples

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.

Hence, 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.

Hence, 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.

Hence, the missing base is 3/4.

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