# FIND THE MISSING EXPONENT

Find the missing exponent :

Exponent means how many times its base is used as a factor.

Step 1 :

To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.

Step 2 :

On both sides, powers have the same base, so their exponents must be equal.

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

## Find the missing exponent - Examples

Problem 1 :

Write the missing exponent Solution :

Let "x" be the missing exponent

Step 1 :

To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.

That is, Hence, the missing exponent is 2.

Problem 2 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we write 8 as the multiple of 2.

That is,

8  =  2 x 2 x 2 = 2³

2³ = 2^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 3.

Problem 3 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we write 100 as the multiple of 10.

That is,

100  =  10 x 10  =  10²

10² = 10^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 2.

Problem 4 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we write 27 as the multiple of 3.

That is,

27  =  3 x 3 x 3  =  3³

3³ = 3^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 3.

Problem 5 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we have to write 1 and 169 as the multiple of 1 and 13 respectively.

1 = 1 x 1 = 1²

169 = 13 x 13 = 13²

(1/169) = (1²/13²) = (1/13)²

(1/13)² = (1/13) ^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 2.

Problem 6 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

We can consider 14 as 14 raised to the power 1.

That is,

14¹ = 14^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 1.

Problem 7 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we have to write 64 and 81 as the multiple of 8 and 9 respectively.

64 = 8 x 8 = 8²

81 = 9 x 9 = 9²

(64/81) = (8²/9²) = (8/9)²

(8/9)² = (8/9) ^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 2.

Problem 8 :

Write the missing exponent Solution :

Let "x" be the missing exponent.

Now we write 32 as the multiple of 2.

That is,

32  =  2 x 2 x 2 x 2 x 2  =  2

2⁵  = 2^x

Powers have the same base, so their exponents must be equal.

Hence, the missing exponent is 5.

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