**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.

**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.

- Generating equivalent numerical expressions
- Use repeated multiplication
- Division facts
- Exponents
- Using exponents
- Finding the value of a power
- Finding the value of each power
- Find the missing exponent
- Find the missing base
- Finding the factors of a number
- Finding the prime factorization of a number
- using ladder diagram for prime factorization
- Order of operations
- Exploring the order of operations
- Evaluating the numerical expression
- Using exponents with parentheses

After having gone through the stuff given above, we hope that the students would have understood "Find the missing base of an exponent".

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