# FIND THE MISSING EXPONENT WORKSHEET

Problem 1 :

Find the missing exponent.

Problem 2 :

Find the missing exponent.

Problem 3 :

Find the missing exponent.

Problem 4 :

Find the missing exponent.

Problem 5 :

Find the missing exponent.

Problem 6 :

Find the missing exponent.

Problem 7 :

Find the missing exponent.

Problem 8 :

Find the missing exponent.

## Solutions

Problem 1 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

25  =  5x

To get the same base on both sides, write 25 in terms of 5 using exponent.

5=  5x

Equate the exponents.

2  =  x

So, the missing exponent is 2.

Problem 2 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

8  =  2x

To get the same base on both sides, write 8 in terms of 2 using exponent.

23  =  2x

Equate the exponents.

3  =  x

So, the missing exponent is 3.

Problem 3 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

100  =  10x

To get the same base on both sides, write 100 in terms of 10 using exponent.

102  =  10x

Equate the exponents.

2  =  x

So, the missing exponent is 2.

Problem 4 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

27  =  3x

To get the same base on both sides, write 27 in terms of 3 using exponent.

33  =  3x

Equate the exponents.

3  =  x

So, the missing exponent is 3.

Problem 5 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

1/169  =  (1/13)x

Write 169 in terms of 13 using exponent.

1/132  =  (1/13)x

13-2  =  (13-1)x

13-2  =  13-x

Equate the exponents.

-2  =  -x

Multiply each side by (-1).

2  =  x

So, the missing exponent is 2.

Problem 6 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

14  =  14x

Already, we have the same on both sides.

141  =  14x

Equate the exponents.

1  =  x

So, the missing exponent is 1.

Problem 7 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

64/81  =  (8/9)x

Write 64 in terms 8 and 81 in terms of 9 using exponent.

82 / 92  =  (8/9)x

(8/ 9)2  =  (8/9)x

Equate the exponents.

2  =  x

So, the missing exponent is 2.

Problem 8 :

Find the missing exponent.

Solution :

Let 'x' be the missing exponent.

Then,

32  =  2x

Write 32 in terms of 2 using exponent.

25  =  2x

Equate the exponents.

5  =  x

So, the missing exponent is 5.

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